Fund Management

 

Introduction

Not every investor has the time or expertise to manage their own financial assets. As a result, some investors choose to hire a professional manager to manage their investments in the form of a mutual fund or a hedge fund. These investment allow investors to instantly diversify their portfolio and receive professional management. Mutual funds are typically used by smaller investors, whereas hedge funds are designed for wealthy investors. As hedge funds are limited to those who can afford to lose their investments, hence they are subject to fewer regulations. Let's go deep dive in each of these fund management.

Mutual Funds

• Mutual funds are a pool of money collected from many investors where the funds are used to invest in securities such as stocks and bonds.
• Here the desire to have investment expertise rather than put the time and effort into the investment process themselves.
• Usually here the investing of money is on behalf of relatively small investors.
• The portfolio of investments is operated by a manager whose mandate is to generate income or capital gain for the investors.
• A mutual fund has strict investment objectives which must be followed by the manager all the time. These objectives are laid down in the fund's prospectus.
• When investing in a mutual fund, you may come across two types of fees:
• Front-end load is a fee that the fund charges when you buy shares for the first time. The fee often goes to the brokers that sell the fund to investors. This fee is limited to less than 8.5% of the total investment in the United States.
• Back-end load is the fee that the fund charges when you sell your shares. The amount of back-end load decreases with the duration for which you held the shares in the fund. Back-end load fees are generally an attempt to prevent investors from moving quickly in and out of the mutual fund, which increases the expense ratio of the fund. Often, back-end load fees are for a specified period, such as 6-months or 1-year. Once the investor has met the holding period requirements, back-end load fees typically go away.
• As this accept investments from retail investors they are subjected to higher level of regulation.
• Net Asset Value (NAV)
• The Net Asset Value (NAV) of a mutual fund is the per-unit market value of all its securities and cash, minus its liabilities, divided by the total number of outstanding units.
• NAV is calculated on a daily basis and represents the price at which investors buy or sell units of the mutual fund.  
• Here is the formula to calculate NAV:  
• NAV = Market Value of Assets − Liabilities / Number of Outstanding Units​
• Market Value of Assets, includes the current market value of all the securities held by the mutual fund. For stocks, it is the market value of each stock in the portfolio, for bonds, it is the market value of the bonds and so on.
• Liabilities, represent any outstanding costs or obligations that the mutual fund needs to cover. This could include expenses, fees, or any other outstanding payments.
• Number of Outstanding Units, is the total number of units (shares) issued by the mutual fund that are currently held by investors.
• Example:
• If the total value of the all the assets in the fund is calculated to be $100 million, $50 million as liabilities and if the number of outstanding shares is 2 million, then NAV is $25 per share (=100-50/2).
• If investor wants to invest $1000 they would exactly buy 40 shares (=1000/25) on the relevant trading day.
• It's important to note that NAV is usually calculated at the end of each trading day since mutual funds are typically valued once a day after the market closes. Investors use the NAV to determine the price at which they can buy or sell shares in the mutual fund. The NAV per share is the value at which investors transact with the mutual fund.
• There are different types of mutual funds, such as:
• Index Funds
• Open-End Mutual Funds
• Close-End Mutual Funds
• Exchange Trade Funds
• The main differences between them revolve around how they issue and redeem shares, how they are traded, and their pricing mechanisms.
• There are no tax advantages associated with investments in mutual funds, as though he or she owns the investments of the funds. For example, if the shares are by the fund at USD 70 and sold at USD 90, the investor has a USD 20 capital gain that is subject to taxation.

Index Funds

• An index fund is a specific type of mutual fund that aims to replicate the performance of a particular financial market index. 
• Instead of actively selecting and managing individual securities, index funds designed  to passively track the performance of a specific index, such as the S&P 500, the Dow Jones Industrial Average, FTSE 100 or others.
• Tracking can be done by following:
• Buying all the shares in the index in amounts that reflect their weight in the index
• Choosing a smaller portfolio of representative stocks that have been proven to follow the index
• Using index futures
• Tracking error measures how well a fund tracks its intended index.

Open-End Mutual Funds

• Open-end funds continuously issue and redeem shares based on investor demand. This means that investors can buy or sell shares directly from the fund at the current net asset value (NAV) per share, which is calculated at the end of each trading day. 
• The number of shares and the size of the fund expand and contract as investors chose to buy and sell shares, leading number of shares increase or decrease.
• In an open-end fund, one deals with the funds itself when buying shares.
• Shares can be bought or sold back to the fund at any time, and available for subscription throughout the years.
• They are valued once a day, at 4 p.m in EST. When an investor issues instructions to buy or sell shares, the value calculated at the end of the day which is the next available NAV.
• If an investor who decides to buy share at 10:00am will enter a buy order for a set dollar amount, but they will not know the price at which they will transact until after the market closes. Transactions are executed at the end of the day after NAV calculation. 
• Hence open-end mutual funds have very low price transparency because they trade at the next available NAV. 
• Since shares are transacted at an unknown price, investors cannot use stop order or limit orders.
• When the investors decide that they want to exit their investment in an open-end mutual fund, they can redeem their shares directly from the fund company, who either send them  through cheque or a digital transfer of the value of the investment.
• The total number of shares outstanding goes up as investors buy more shares and goes down as shares are redeemed.
• At a high level, the open-end mutual funds are broken down into four main categories:
• Money markets funds, invest in short-term interest bearing instruments such as treasury bills, commercial paper, certificates of deposit, banker's acceptance and other highly liquid and low-risk instruments. These funds are designed to provide investors with a safe and easily accessible place to park their cash while earning a modest level of interest, hence the risk is lower. For many investors money market funds are alternative to a savings account at a bank, and the return on money market funds is usually higher than on bank deposits. Most money market funds attempt to keep a NAV of $1. When the fund drops below $1 NAV, it is referred to as breaking the buck. Breaking the buck occurs very infrequently. 
• Equity funds, invest solely in stocks. Within this category, one can find index funds that track a broad market index. Equity funds can be divided into two general groups:
• Actively managed fund. An actively managed fund relies on stock selection and timing skills of the fund manager, such as funds that invest in equities with high dividend ratios. Actively managed funds usually have a higher expense ratio than a passively managed fund, where the expense ratio is defined as total expenses divided by total assets. 
• Index or passively managed fund. An index or passively managed fund is designed to track an index, such as the S&P 500 or FTSE 100. The fund buys all the shares in the index in an amount representative of the index’s weight and generally accomplishes this goal. Although index funds attempt to perfectly track the index of stocks, tracking is not perfect, as every index fund has tracking error. Index funds typically have lower expense ratios compared to actively managed funds.
• Bond funds, invest only in fixed income instruments such as sovereign debt, corporate bonds, and asset backed securities.
• Hybrid funds, will blend stock and bond ownership into same fund.
• Taxation of open-end mutual fund:
• In an open-end mutual fund, the investor pays tax as though he owned the securities in which the fund has invested. When the fund receives a dividend, an investor has to pay tax on his share of the dividend, even if the dividend is reinvested in the fund for the investor.
• When the fund sells securities, the investor is made to realize an immediate capital gain or loss, even if the he has not sold any of his shares in the fund.
• Open-end mutual fund have a management fee and a sales charge, which are commonly called as loads. 
• Open-end mutual fund this not listed on a stock exchange, transactions occur directly through the fund.
• Maturity is not fixed and the corpus is variable.

Closed-End Mutual Funds

• Closed-end funds have a fixed number of shares that are issued. 
• These are issued through an initial public offering (IPO). After the IPO, the shares are traded on stock exchanges like individual stocks. After the initial shares no more shares are issued.
• In a closed end mutual fund, trade at market prices, allowing the shares to potentially buy share at a discount or sell at a premium to their NAV. The reason behind this is that shares are publicly traded on an exchange, and therefore the price is a function of supply and demand.
• For closed-end funds, two NAVs can be calculated.
• Price at which the shares of the fund are trading.
• Fair market value: market value of the fund’s portfolio divided by the number of shares outstanding. Usually a closed-end fund’s share price is less than its fair market value. Fees paid to fund managers are considered to be a reason for this.
• Selling price is Premium / discount to NAV.
• Like regular corporations and the shares of the fund are traded on a stock exchange which means they can be bought and sold during any time of the day. But these are available for subscription only during a few specified days and only long positions can be taken.
• Transactions are executed in real time, which means they have better price visibility and can utilize stop orders and limit orders if they so choose.
• Unlike open-ended here do not transact directly with the fund company, rather the shares are bought and sold through brokers or with other investors.
• Here this is listed on an exchange for trading.
• Maturity is fixed, in general 3-5years and corpus is fixed.

Exchange Traded Funds

• ETFs are innovation twist on the open-end and close-end mutual funds. Enabling instance diversification like an open-end fund but they are exchange-traded, which means they trade throughout the day on the open market just as closed-end fund does.
• Created by institutional investors. 
• Most track an index; e.g., SPDR tracks the S&P 500
• Some or all of the shares in the ETF are traded on a stock exchange characteristics of a closed-end fund but differs as institutions can exchange ETF shares for the underlying assets or even deposit new assets in return receive shares, and there is never a material difference between ETF exchange-traded share price and its fair market value (FMV).
• ETFs typically trade at their NAV.
• ETFs can be bought or sold at any time of the day, hence are more liquid. 
• ETFs can utilize stop orders, limit orders and even short sell just like a stock.
• Short selling is a different strategy. In this case, an investor borrows shares of an ETF (or stock) from a broker and sells them on the open market with the hope that the prices will go down.
• Later, they aim to buy back the same number of shares at a lower price, return them to the lender (the broker), and pocket the difference as profit.
• ETF holdings are disclosed twice a day thereby providing investors with more information and tremendous visibility about assets underlying the fund unlike open-end mutual funds which disclose their holdings relatively infrequently.
• ETFs in general have lower expense ratios.

Undesirable Trading Behaviours at Mutual Funds

• Some of the potential undesirable behaviours among mutual funds include late trading, market timings, front running and directed brokerage.
• Late Trading
• Late trading refers to the illegal practice and subject to prosecution of buying or selling mutual fund shares after the market closes, but at the price determined at the close of trading.
• For example, here the orders are accepted after the 4.00pm EST cut off trading time, but gets the NAV (Net Asset Value) calculated based on the closing prices.
• Market Timing
• Market timing is the strategy of trying to predict the future movements in an attempt to make profit from the financial markets by either buy or sell decisions based on short-term price fluctuations in the market. Investors using market timing attempt to enter or exit the market at specific times they believe will be advantageous.
• Although potential concern to regulators if trading exceptions are made for market timing, the act of market timing is not illegal.
• Layman Example:
• Imagine you have a friend named Alex who is trying to use market timing to make money in the stock market.  
• Alex's Belief: Alex believes that stocks are going to go up in the next few weeks because of positive news about a new technology product. So, Alex decides to invest a significant portion of their savings in a mutual fund that tracks the stock market. Market 
• Timing Action: Alex closely follows financial news and economic indicators to predict when the stock market might reach its peak. Alex believes that once the market has peaked, it's likely to go down. Therefore, Alex plans to sell the mutual fund shares just before the expected market decline. 
• Outcome: If Alex's prediction is correct and the market does indeed go up, Alex might make a profit by selling the mutual fund shares at a higher price. However, if the prediction is wrong, and the market does not behave as expected, Alex might end up selling at a loss or missing potential gains if the market continues to rise.
• Market timing is challenging because accurately predicting short-term market movements is difficult, even for experienced investors.
• Front Running
• Front Running involves in trading ahead of a likely price increase or decrease due to a known upcoming trade made by the fund. It may involve the trader's own account or favoured clients or employees.
• Like late trading, front trading is also illegal and is subject to prosecution.
• An example, a broker learns that a large client is about to place a substantial order to buy a specific mutual fund. The broker buys shares of that fund for their personal account before executing the client's order, expecting the price to rise due to the client's upcoming transaction.
• Directed Brokerage
• Directed Brokerage, involves quid pro quo whereby a mutual fund will direct trades to broker in exchange for the broker investing its clients in the mutual fund.
• Although this is not illegal, but strongly discouraged practise.
• Let's see an example, an investment adviser directs a mutual fund to use a particular brokerage firm to execute the fund's trades, possibly because the adviser receives some form of compensation or benefit from that brokerage.

Hedge Funds

• Mutual funds are marketed to all the investors, while hedge funds are restricted to only wealthy and sophisticated investors and institutions, to attract funds from wealthy individuals and large investors such as pension funds.
• Free from regulations and are given more flexibility in terms of investment strategies. Although some restrictions are imposed by their prime broker, the bank that provides hedge funds with financing and trade processing.
• Hedge funds charge investors higher management or operation fee, in general hedge fund fees, are observed as below:
• An annual management fee of 1%-3%  of assets
• An incentive fee of 15%-30% of realized net profits
• But typically a hedge fund fee might be read as “2 plus 20” indicating that the fund charges 2% per year of assets under management and 20% of net profit. 
• In addition to high fees, there is usually a lock up period (cannot withdraw) of at least one year. 
• A lockup period exists for a reason - many hedge fund investments are not easy to unwind on short notice. Some hedge fund investment are illliquid, which means managers cannot sell them quickly and retain a proper value. 
• In addition some hedge fund investments are bet on certain asset mispricing, and those trades can take time to unwind.
• Hedge funds are not listed on an exchange.

Prime Brokers

• Prime brokers act as intermediaries between hedge funds and various financial markets.
• A prime broker is a financial institution (which is often a bank) that provides a suite of services to hedge funds and other institutional clients. 
• These services are designed to facilitate the operational and trading activities and lending of the hedge fund, also provide risk management. 
• Prime brokers further more can carry out stress tests on the hedge fund's portfolio to decide how much it is prepared to lend. The hedge fund can then post its securities with the bank as collateral.
• As mentioned, hedge funds are subject to very little regulations, the prime broker will reduce the borrowing limit of the hedge fund and force it to close out the positions.
• Some hedge fund strategies can be certain to make money in the long term while risking short term losses, if this losses occur prime brokers would require addition collateral.
• Large hedge funds may use more than one prime broker.

Hedge Fund Expected Returns and Fee Structure

As a precondition for imposing high incentives fees, investors may be offered several guarantees. These includes the below:

• Hurdle Rate: This is the minimum return that a hedge fund should produce in order for the incentive fee to be applicable. Generally, investors push for hurdle rates that are as high as possible, sometimes even as high as the return on the S&P 500.
• High-water mark clause: This clause indicates that any previous losses must be recouped by new profits before an incentive fee applies. Prior losses may be comprised of performance losses, management fees and administrative fees. The high-water mark will vary among investors. For instance, if an investor places $100 million with a hedge fund and the fund loses $10 million, then the managers of the hedge fund must make $10 million before incentives kick back in.
• Clawback clause: This clause allows investors to apply part or all of previous incentive fees to offset current losses. A portion of the incentive fees paid by the investor each year is then retained in a recovery account so that it can be used to compensate investors for a percentage of any future losses. 
• Proportional adjustment clause: A proportional adjustment clause states that if the investors suffer loss and simultaneously if funds are withdrawn by investors, the amount of previous losses that have to be recouped is adjusted proportionally. In the example used above, if the investor withdraws $5 million before the hedge fund makes up the losses, the hedge fund may only need to make up $5 million before the incentive fees apply again.

Hedge Fund Strategies

Long and Short Equity

• The long and short equity strategy involves in maintaining long and short positions in equity and equity derivative securities.
• The hedge fund manager buys the long position in a group of stocks that are considered undervalued and selling the short position in a group that are considered overvalued by the market. 
• The hedge fund manager may have a net long bias where the longs are bigger than the shorts or a net short bias where the short are bigger than the longs.
• Referring to a fund as long/short captures the broad picture. There are many different styles underneath this umbrella, including:
• An equity-market-neutral fund where longs and shorts are matched.
• A dollar-neutral fund is an equity-market-neutral fund where the dollar amount of the long position equals the dollar amount of the short position.
• A beta-neutral fund is an equity-market-neutral fund where the weighted average beta of the shares in the long portfolio equals the weighted average beta of the shares in the short portfolio so that the overall beta of the portfolio is zero or totally insensitive to market movements.
• A sector neutrality fund, is where long and short positions are balanced by industry sectors.
• A factor neutrality, is where the exposure to factors like the price of oil, the level of interest rates, or the rate of inflation is neutralized.
• In theory, this strategy could provide strong returns regardless of whether general market conditions are in bull and bear markets if the stocks are picked up after being well researched.

Dedicated Short

• A dedicated short hedge fund is a type of investment fund that primarily focuses on making money from the decline in the value of stocks or other assets. Unlike traditional funds that aim for overall market growth, a dedicated short fund specializes in profiting from falling prices.
• At any given time, it is reasonable to suppose that there are as many overvalued share as undervalued shares. This means that short positions take the lion's share of the fund's overall positions.
• Dedicated short hedge funds are focused exclusively on finding a company that they think is overvalued and sell them short. This strategy exploits the fact that brokers and analysts are hesitant to issue sell recommendations. 
• Examples include:
• Companies with weak financials
• Companies that change their auditors regularly
• Companies that delay filing reports with the SEC
• Companies in industries with overcapacity
• Companies attempting to silence their short sellers
• Due to lack of hedging of overall markets, dedicated short funds do not perform well when markets are performing well.

Distressed Securities

• Distressed Securities deals with trades related to distressed securities by calculating a fair value for these securities considering possible future scenarios and their probabilities.
• Bonds with a rating of BB or lower are referred to as “non- investment grade” or “junk” bonds. Bonds with a credit rating of CCC are known as “distressed”. Bonds with a D rating are in default.
• This is an event driven strategy that tends to focus on companies that are at financial trouble.
• Distressed securities cannot be shorted, so managers look for a debt that is undervalued by the market.
• Managers must be well versed with bankruptcy proceedings, since distressed securities are highly susceptible to this condition.
• Passive managers buy distressed debt when the price is below its fair value and wait. The advantage of a passive approach, compared to an active approach, is that the fund generally places smaller bets on the distressed company. 
• Active managers might purchase a large position in outstanding debt claims so that they have the right to influence a reorganization proposal. The risk with this is that the hedge fund is placing more assets at risk for greater control of the assets in case bankruptcy occurs.
• Funds that employ this strategy impose more stringent lock-up and withdrawal terms.

Merger arbitrage

• Merger arbitrage is a bet that a merger or acquisition deal will take place after it has been announced. 
• The goal is to exploit price inefficiencies that may occur before or after a merger.
• Merger-arbitrage hedge funds are observed to generate steady but not huge returns.
• There are two main types of deals: cash deals and share-for-share exchanges.
• Cash Deal
• Consider a cash deal in which Company A announces that it would acquire all the shares of Company B for $30 per share. 
• The shares Company B were trading at $20 earlier and after the deal is announced its price jumps to $28. 
• The price may not have risen as high as $30 because there is a chance that the deal will not go through and also it may take some time to factor into market prices. 
• Merger-arbitrage hedge funds buy the shares in company B for $28 and wait, so that if acquisition happens at $30 or higher, the fund makes a profit of minimum $2 per share or more respectively. 
• However, if deal does not go through, the hedge fund will take a loss.
• Share-for-share
• Consider a share-for-share exchange in which Company A is willing to exchange one of its shares for four of Company B’s shares. 
• Assume that Company B’s shares were earlier trading at 15% of the price of Company A’s. After the announcement, Company B’s share price might rise to 22% of Company A’s share price.
• A hedge fund following a merger-arbitrage strategy would buy a certain amount of Company B’s stock and at the same time short a quarter as much of Company A’s stock to generates profits if the deal consummates.
• In most cases, a merger announcement is followed by a spike in the stock of the acquiring company and a dip in the stock of the target.
• It should be emphasized that merger arbitrage is not about trading on the inside non public information, as this is illegal. It should access the probability of a merger being successful and the likely final price or exchange ratio in the case of share-for-share, at the time of the merger announcement.

Convertible Arbitrage

• Convertible arbitrage strategy seeks to profit from the discrepancies in a company's convertible securities relative to the company's stock.
• This strategy involves taking long position in a convertible bond and hedging it by taking short position in the underlying stock.
• Convertible bonds could be converted into the equity of the bond issuer at a specified times and price in the future.
• The convertible bond price depends on factors such as the price of the underlying equity, its volatility, the level of interest rates, and the chance of the issuer defaulting.
• A hedge fund using the convertible arbitrage strategy develops a complex model for valuing these convertible bonds so as to extract higher returns from it.
• Many convertible bonds trade at prices below their fair value, so hedge fund managers buy the bond and then hedge their risks by shorting the stock.

Fixed Income Arbitrage

• Fixed Income Arbitrage strategy seeks to profit from the discrepancies in related to fixed income instruments.
• At any given time, some traded bonds are likely to be relatively expensive compared with other similar bonds, which other are relatively cheap. In a fixed-income arbitrage strategy, the hedge fund manager buys bonds that seem relatively cheap and shorts the ones that are relatively expensive.
• One of the strategies followed by hedge fund managers in relation to fixed income arbitrage is a relative value strategy, where they buy bonds that the zero-coupon yield curve indicates are undervalued by the market and sell bonds that it indicates are overvalued.
• Market-neutral strategies are similar except that they have no exposure to interest rate movements.
• Some fixed-income hedge fund managers follow directional strategies where they take a position based on beliefs that certain spread between interest rates, or interest rates themselves, will move in a certain direction. Usually they have a lot of leverage and have to post collateral.
• The risk associated with this strategy is that although the strategy may work out well in the long term, in the short term if the market goes against it, loss has to be faced.

Emerging market strategies

• Emerging market strategies engage in investments in developing countries.
• This involves debt/equity investment in emerging markets, that aims to identify emerging market shares that are overvalued or undervalued.
• In case of equities, managers invest in securities trading on the local exchange, or securities like American Depository Receipts (ADRs). 
• In case of debt, hedge funds invest in either Euro bonds or local currency bonds. 
• The price discrepancies between securities and the underlying shares may give rise to arbitrage opportunities. 

Global macro strategies

• Global macro strategies carry out trades that reflect global macroeconomic trends, in general investment decisions guided by the economic or political outlook of a country. 
• Hedge fund managers spot situations where markets have moved away from equilibrium and place large bets that they will move back into equilibrium. 
• For example, the investment focus may be on foreign exchange rates, interest rates or inflation.
• A deviation from equilibrium could take a long time to correct itself and some hedge funds will not be able to wait out of the trend.
• The main risk is that they may be unaware of when equilibrium will be restored because world markets can be in disequilibrium for long periods of time.

Managed futures strategies

• Managed futures strategies try to predict future movements in commodity prices based on manager’s judgment or trading rules generated by computer programs.
• They make bidirectional bets with long/short positions.
• Managers may use technical analysis which analyzes past price patterns to predict the future; or fundamental analysis which involves calculating a fair value for the commodity from fundamental factors.
• Technical analysis typically comprises back-testing, out-of-sample testing, and other data mining techniques. They test their prediction by performing backtest using their trading rules using historical data. But a key drawback of backtesting is that there is no distinction made between strategies that truly worked based on the proper fundamental analysis or strategies that were successful strictly because of luck and subsequently might not have repeated success. It is also important to test a trading strategy out-of-sample, this means that a historical data used to test a strategy should be separate from the historical data used to develop the strategy.
• Fundamental analysis, when managers employ fundamental analysis techniques, they are attempting to derive a fair value for the commodity based upon so-called fundamental factors. Fundamental factors might include: 
• Market conditions in which the fund is investing. 
• The economy.
• Weather conditions, including projected weather conditions.
• Supply and demand forces. 
• Cross-competition from other commodities

Hedge Fund Performance

• It is common for hedge funds report good returns for a few years and then perform poorly all of a sudden only to close their business eventually. 
• There is a general view that hedge fund returns are like the returns from writing out-of-the-money options: the options cost nothing, but occasionally they become very expensive. 
• The Tass hedge funds database includes only hedge funds that report voluntarily. 
• Excludes small hedge funds and those with poor track records over the years do not report their returns and are therefore not included in the data set. Only good funds are included. The resulting performance analysis is thus inherently biased.
• When returns are reported by a hedge fund, the database is backfilled with the fund’s previous returns. This creates a bias in the returns that are in the data set because only the hedge funds that do well are the ones that disclose their return data. When this bias is removed, it is observed that hedge fund returns are no different from mutual fund returns, especially when their fees are taken into account.
• Measurement bias, participation in hedge funds indices is voluntary. If the fund had good performance, then they will report their results to the index vendor. If not given good results, then they simply do not report their result to the index. Hence there is measurement bias is there in hedge fund indexing.
• Backfill bias refers to the potential distortion in the performance history of a hedge fund caused by including historical performance data for periods before the fund officially reports to a performance database. When returns are reported by a hedge fund, the database is then backfilled with the fund's previous returns. It creates an issue with reliability for hedge fund benchmarks.

Hedge Fund Risks

• Liquidity Risk
• It occurs when the fund invests in illiquid assets.
• Liquidity is the function of the below:
• size of the position
• intrinsic liquidity of the instrument
• Pricing Risk
• Some of the assets are quite difficult to price like derivatives.
• Counterparty Risk
• The manager gets into contracts with dealers, brokers and clearing agents. 
• There is always a risk that these parties will renege on their obligations, putting the funds on the path of unprecedented losses.
• Short Squeeze Risk
• The fund manager may be forced to purchase a security they had sold short sooner than anticipated when the investor from whom the security was borrowed comes calling early.
• Settlement Risk
• One or more parties in a transaction may fail to deliver securities as per the contract.

Hedge Fund Calculation

Formula:

Hedge fund’s fee =  I + M

Here,

I = Investment Fees, ideally 20% (0.2)

M = Management Fees, ideally 2% (0.02)

Example1:

Let's consider a hypothetical hedge fund with a starting Net Asset Value (NAV) of $100 million.

Management Fee Calculation:

1. • Assuming the monthly average AUM (Assets Under Management) is $100 million for the month.
   • Management Fee = (2% × $100 million) / 12 = $166,667 (monthly management fee).

Incentive Fee Calculation:

1. • Assuming the fund generated a 5% return for the month.
   • Management Fee Adjusted Returns = Fund's Monthly Returns - Management Fee
   • Management Fee Adjusted Returns = 5% - 2% = 3%
   • Incentive Fee = 20% × 3% = 0.6%

Total Fees for the Month:

• Total Fees = Management Fee + Incentive Fee
• Total Fees = $166,667 (Management Fee) + 0.6% × $100 million (Incentive Fee)
• Total Fees = $166,667 + $600,000
• Total Fees = $766,667

Example2:

An example of a hedge fund manager’s incentive. As an example of the incentive structure of a hedge fund manager, consider this example. Suppose there is a 40% probability of a 60% profit and a 60% probability of a 60% loss for a hedge fund that charges the theoretical industry-standard fee of “2 plus 20%.”

In this example, the expected return on the investment is -12%.

= 0.4 ∙60% + 0.6 ∙(− 60% ) = − 12%

Interestingly, although the return is negative, the hedge fund manager still earns a fee from managing the money (as is the case with mutual fund managers and most other financial mangers). In this example, the fee income is 13.6% of the assets under management for the case when the fund earns a 60% profit and 2% if the -60% materializes. The probability- weighted fee (expected value) is 6.64%, made up of the 2% management fee and the 4.64% incentive fee. Of course, a mutual fund manager would have also been paid regardless of the return of the fund.

• 60% profit example: the hedge fund’s fee is 2% + 0.2 × 58% (60% - 2%) = 13.6%.
• 60% is probability of profit
• 2% is management fee
• .2 or 20% is incentive fee
• 60% loss example: the hedge fund’s fee is 2% + 0.2 x 0% = 2%.
• The expected (or probability weighted average) fee to the hedge fund is 0.4 × 13.6% + 0.6 × 2% = 6.64%.

The expected return for the hedge fund investors, after accounting for the fees, is -18.64%, as shown in the table below.

•  0.4∙(60%−13.6%)+0.6∙(−60% −2%) = −18.64%

An Example of a High-Risk Investment with a "2 + 20" Fee Structure 

• Returns: 60% and -60% 
• Probability: 40% and 60%
• Expected return to hedge fund: 6.64% 
• Expected return to investors: -18.64% 
• Overall expected return: -12.00%

Example3:

What is the expected payoff for fees if a hedge fund uses a standard 2 plus 20% incentive fee structure with an investment that has a 35% probability of making 55% and a 65% probability of losing 45%.

• The expected return on the investment is −10%.
• = 0.35 ∙55% + 0.65 ∙(−45% ) = −10%
• 55% profit example: the hedge fund’s fee is 2% + 0.2 × 53% (55% - 2%) = 12.6%.
• 60% is probability of profit
• 2% is management fee
• .2 or 20% is incentive fee
• 45% loss example: the hedge fund’s fee is 2% + 0.2 x 0% = 2%.
• The expected (or probability weighted average) fee to the hedge fund is 5.71%.
• = 0.35 × 12.6% + 0.65 × 2% = 5.71%
• The expected return for the hedge fund investors, after accounting for the fees, is -15.71%
• 0.35∙(55%−12.6%) + 0.65∙(−45% −2%) = −15.71%

Mutual Fund VS Hedge Fund

Mutual Fund

• Size of the investor, mutual funds may cater to small or large investors, and typically have different classes of shares depending upon the size of the investor.
• Disclose of investment strategy, mutual funds must be generally transparent with their investment strategy.
• Risk, the risk is dependent upon the allowable investment options stated in the prospectus.
• Fees, usually has management fees as a percentage of assets under management and potentially front-end and/or back-end loaded fees.
• Flexibility, managers has a lots of constraints to deal in their investment strategies, regulatory environment and fund structure. Can invest in various asset classes, including equities, bonds, commodities, and other investment options. One strategy that is prohibited is the use of leverage.
• Regulations, high regulations.
• Redemption, mutual funds or ETFs allow investors to redeem or sell their shares on any given day. Mutual funds may charge a fee for short-term trading or a back-end load fee.
• Paperwork, offered via prospectus.
• Liquidity, investors can withdraw their money any day.
• Reporting of fund value, mutual funds are required to report their NAV at least once per day.
• Self investments, managers does not have to put some of their capital in the fund.
• Advertisement, may advertise freely.
• Listing, maybe listed (close-end funds).
• Assessment, generally easy and objective to measure. 

Hedge Fund

• Size of the investor, typically hedge fund investors must be accredited investors.
• Disclose of investment strategy, hedge funds generally keep their investment strategy proprietary, as they consider this a competitive advantage. Hedge funds must disclose the general nature of their investment activities but keep proprietary components proprietary. Additionally, as long as it is disclosed, hedge funds may switch between investment strategies depending upon management’s view of the economic situation.
• Risk, can range from very risky to completely hedged. Hedge funds are generally considered riskier than mutual funds because of the investment strategies employed.
• Fees, usually higher fees that, including base fees and fees linked to performance of the fund.
• Flexibility, managers has a fewer constraints to deal in their investment strategies, regulatory environment and fund structure. Can use leverage, sell short or even use derivates.
• Derivatives:
• Definition: Derivatives are financial instruments whose value is derived from the value of an underlying asset, index, rate, or other financial instruments. They derive their value from the performance of an underlying entity and include options, futures, forwards, and swaps.
• Examples:
• Options: Contracts that give the holder the right (but not the obligation) to buy or sell an asset at a predetermined price within a specified period.
• Futures: Contracts to buy or sell an asset at a future date for a price agreed upon today.
• Swaps: Agreements where two parties exchange cash flows or other financial instruments over a specific period.
• Key Points:
• Investors use derivatives for various purposes, including hedging against market fluctuations, speculating on price movements, and managing risk in their portfolios.
• While derivatives can be valuable tools, they can also be complex and carry risks, including the potential for significant losses.
• Leverage:
• Definition: Leverage refers to the use of borrowed funds to increase the size of an investment or position beyond what would be possible with one's own capital. It magnifies both potential gains and losses.
• Examples:
• Margin Trading: Borrowing money from a broker to buy securities, with the securities serving as collateral for the loan.
• Options Trading: Using options contracts to control a larger amount of an underlying asset with a smaller upfront investment.
• Key Points:
• Leverage can amplify returns, allowing investors to control a larger position with a smaller amount of capital.
• However, it also increases the risk, as losses are also magnified. If the market moves against the investor, the losses can exceed the initial investment.
• Sell Short:
• Definition: "Selling short" or "short selling" is an investment strategy where an investor sells a financial instrument (such as stocks) that they do not currently own. In a short sale, the investor anticipates that the price of the financial instrument will decline, allowing them to buy it back later at a lower price. The goal is to profit from the difference between the higher selling price and the lower buying price.
• Here's a step-by-step explanation of how short selling works:
• Borrowing the Asset: The investor borrows shares of a stock (or other securities) from a broker with the agreement to return the same number of shares at a later date. This is typically facilitated through the brokerage's margin account.
• Selling the Borrowed Asset: The investor sells the borrowed shares in the open market. This creates a short position, where the investor is effectively "short" the stock.
• Waiting for Price to Decline: The investor hopes that the price of the stock will fall before they have to return the borrowed shares.
• Buying Back the Asset: If the price does decline as anticipated, the investor buys back the same number of shares in the open market at the lower price.
• Returning the Borrowed Shares: The investor returns the borrowed shares to the broker.
• Profit or Loss: The profit or loss is the difference between the selling price (initial short sale) and the buying price (covering the short position). If the stock price drops, the investor makes a profit; if it rises, the investor incurs a loss.
• Examples:
• Let's say an investor believes that Company XYZ's stock, currently trading at $50 per share, is overvalued and will decline in the near future. 
• The investor borrows 100 shares from a broker and sells them in the market, generating $5,000 ($50 x 100 shares) in cash. 
• If the stock price drops to $40, the investor buys back 100 shares for $4,000 ($40 x 100 shares) and returns them to the broker. 
• The investor's profit would be $1,000 ($5,000 initial cash - $4,000 to buy back shares).
• Key Points:
• Short selling involves betting on a decline in the price of an asset.
• It's a strategy that carries significant risks, as there's no limit to how much the price of the asset can rise.
• Short selling is typically done in the context of a margin account, as it involves borrowing assets.
• Short selling is a more advanced investment strategy and is not suitable for all investors. It requires a good understanding of the market, careful risk management, and the ability to react quickly to changing conditions. 
• Additionally, short selling is subject to regulatory rules, and there are restrictions on certain types of short sales to prevent market manipulation.
• Regulations, fewer regulations than mutual funds.
• Redemptions, hedge funds often have long lock-up periods. During lock-up periods, investors cannot withdraw their money.
• Paperwork, offered via private placement memorandum.
• Liquidity, investors can only get their money periodically.
• Reporting of fund value, hedge funds have more flexibility in reporting returns monthly, quarterly, or at some other interval.
• Self investments, as a sign of good faith, the manager is expected to put some of their money in the fund.
• Advertisement, no free to advertise in the public.
• Listing, cannot be listed on an exchange.
• Assessment, generally problematic due to measurement bias and backfill bias.

Credits and References

• GARP, Schweser and Bionic Turtle Notes
• https://www.investopedia.com/
• http://chat.openai.com/ #shout out to the examples helped in learning the concepts in depth.

Insurance Companies and Pension Plans

 

Whether you face flood or fire, theft or sickness and for any such mishap the first thing we discuss is do we have insurance. Let's see how the insurance and pension world works!

Insurance

Insurance is an agreement between an insurer and a policyholder, where the insurer receives protection from any loss events in exchange for the payment of the periodic premiums. 

There are in general three categories of insurance - life insurance, non life (property and casualty) insurance and health insurance.

Life Insurance

Interesting Note: As we cannot put a price or tag on human life, the word "insurance" is replaced with assurance. -- Professor James Forjan

• Life insurance companies provide a long term coverage and make a specified payment when a policyholder's life is at risk, which implies the death of a policyholder, this includes natural death (i.e. certain) or accidental death (i.e. uncertain).
• Types of life insurance policies:
• Term life insurance: 
• A term life insurance, is a contract to pay the beneficiary a predetermined amount of benefit, also called the sum assured, in case the policyholder dies with the term of contract. 
• Here pays only if the policyholder dies during a certain fixed period. 
• The mortality tables are used to calculate breakeven premium.
• For example, when you take out a mortgage loan, it's often a good idea to also take out term life insurance. This can provide a safety net in case any unexpected events occur and you are unable to pay back the loan. Term life insurance typically provides coverage for a specific period of time, so it's important to choose a policy that aligns with the term of your mortgage. That way, you can have peace of mind knowing that your loved ones will be taken care of if anything were to happen to you.
• Term life insurance policies usually have a constant or declining face value over time. 
• When a premium is not constant over the years of the contract, the policy is referred to as an annual renewable term policy. 
• In an annual renewable term policy, the policyholder renews the policy at the rate that reflects the age of the policymaker regardless of the policymaker’s health. 
• Whole life insurance:
• Provides protection for the life of the policyholder, so it provides a payoff on the death of the insured, regardless of when it happens.
• Premiums are in general paid throughout the life of the policyholder.
• Variable life insurance: 
• A variable life insurance policy is a type of whole life policy insurance with an investment component.
• The surplus premium are invested in a fund chosen by the policyholder e.g. bonds, equities or money market fund.
• The total benefit received on the death of the policyholder will be sum assured plus a variable amount generated from the investment account.
• Universal life insurance: 
• A universal life insurance policy is a type of whole life policy insurance.
• Normally if the policyholder stops making premium payments, the policy no longer provides coverage and the policy is then referred to as lapsing. Here it provides lot more flexibility in the term of the premium payable. 
• The policyholder can reduce the premium down to a special minimum without lapse in coverage.
• While reducing the premium reduces the benefits it does but not as said result in the policy lapsing.
• Variable universal life insurance: 
• A variable universal life insurance policy is a type of whole life policy insurance with an investment component.
• The policyholder can choose between number of alternatives for the investment of surplus premiums.
• Endowment life insurance:
• Last for a specified period and pays a lump sum when the policyholder dies or at the end of the period, whichever comes first.
• There are many variants of endowment life insurance, such as payouts are made when policyholder suffers from critical illness.
• In a unit linked endowment policy, the policyholder chooses a fund, and the payout depends on the performance of that fund.
• In a profits endowment policy, where the insurance company announces periodic bonuses depending upon the performance of the investments. The bonuses are reinvested and are paid out at the end of the life of the policy.
• Group life insurance: 
• Covers several people under a single policy and is often purchased by the company for its employees.
• The policy could be contributory, in which case the premium is shared between the employer and employee.
• Other wise, non contributory in which employee has to pay the full premium amount.
• Risk is involved for group insurance as it does not require medical exams, resulting in good and bad risks being taken.
• Annuity contract:
• An annuity contract requires the policyholder to pay lump sum, in returns the policy holder receives a regular series of payments at specified points in future.
• The insurance company funds the annuity by investing the lump sum in an investment of their choice, including securing bonds and mutual funds.
• An annuity helps the policyholder to defer the tax payable until they receive each scheduled annuity payment and may policy holders have relatively low marginal tax rates when the annuity is received.
• Some annuities begin immediately while others start on agreed upon numbers of years later such is also called as deferred annuities. This deferred annuity structure allows the insurance company to invest the funds and build up larger balances in anticipation of payments.
• The amount to which the policyholder's funds grow in an annuity contract is referred to as the accumulation value.
• Depending on the terms of the contract, the accumulation value may be withdrawn prematurely but likely with penalties. Also, increasingly popular are penalty-free withdrawals where the policyholder can withdraw a certain portion of their accumulation value without penalty.
• Usually, if a policyholder dies before annuity payments begin, the full accumulation value can be withdrawn penalty-free.

Property and Casualty Insurance

Property and Casualty insurance companies usually provide annual and renewable coverage against loss events. The premiums may vary either increase or decrease based on any changes in the expected payouts. 

Can be subdivided based on their concentration of activities in either property insurance and casualty insurance.

• Property Insurance: Provide protection against loss of or damage to property from accidents, fire, theft, water damage, etc.
• Casualty Insurance: Covers third party liability (such as injuries sustained on policyholder's premises or accident using the policyholder's use of vehicle) and provides protection individuals and companies against legal liability exposures.

Contracts usually last for a year, but they may be renewed every year. Premiums collected may change, either increase or decrease each year depending upon the expected payouts, profit margins, and competition, among other factors.

The contracts whose payouts are difficult to predict are those where a specific event is liable to trigger claims by many policyholders around the same time.

Most likely here the risks can be controlled by estimating the expected payouts on claims with a high degree of confidence. This is possible when many policies are written in thousands of independent events, such as in automobile insurance. When insurers may face catastrophe risks due to natural disasters, which can lead to many large claims in certain part, while in others they may benefit if there are no natural disasters. Catastrophe risks are all-or-nothing, and can be managed by using geographical, seismographic, and meteorological information to determine the probability and severity of catastrophic events.

In general, for property-casualty insurance companies, property damage claims from natural disasters and liability insurance claims are subject to fluctuating payouts and are very challenging to predict.

The property-casualty insurance company must keep more equity capital as a percent of total assets, than a life company insurance.

Property and casualty insurance company compute the following ratios:

• Loss Ratio: 
• For a given year is the percentage of payouts versus premiums generated. 
• The high loss ratio indicates poor financial health, could be either insurer may not be collecting enough premium to pay claims, expenses and still make a sizeable profit.
• Expense Ratio: 
• For a given year is the percentage of expenses versus premiums generated. 
• It shows how efficient the insurer is in terms of cash management before factoring in claims and investment gains or losses.
• The largest expenses are usually loss adjustments (e.g. claims investigation and assessing payout amounts) and selling (e.g. broker commissions).
• Combined Ratio: 
• For a given year is equal to the sum of the loss ratio and the expense ratio. 
• For example, for a category of policies in a particular year, if the loss ratio is 75% and the expense ratio is 30%, then the combined ratio is 105%.
• Combined Ratio after dividends: 
• For a given year is equal to the combined ratio plus the payouts of dividends to policyholders as a percentage of premiums only if applicable. 
• From the above example, suppose a small dividend to the tune of 1% of premiums is paid to the policyholders, we get a combined ratio after dividends of 106%.
• Operating Ratio: 
• For a given year is the combined ratio (after dividends) less investment income as a percentage of premiums. 
• Also could say as is the ratio obtained when investment income earned from premiums is reduced from the losses as represented by the combined ratio. 
• Continuing with the example, our combined ratio after dividends was 106%, which means the insurance company makes a loss of 6% before tax on the policies being considered. If the investment income is 9% of premiums received. Then, the operating ratio would be 106 − 9 = 97%.

Risks associated with property and casualty insurance contracts can be divided into two main risk groups.

• Easy to predict payouts: Payouts with ample historical data allow for accurate predictions, e.g. car accidents and property damage.
• Difficult to predict payouts: Catastrophic risks involve single events such as hurricanes, floods, or earthquakes that may result in many individual claims. These events are known as high consequence, low probability events. Catastrophic claims are not independent of each other, and they are usually all-or-nothing risks. Because of the potentially large claims associated with these risks, property-casualty insurance companies are required to keep more equity capital as a percentage of total assets compared to life insurance companies. Here e.g. earthquakes, floods and hurricanes.

Health Insurance

• Health insurance companies provide coverage to policyholders for medical services that are not covered under a publicly funded health care system.
• Healthcare payment and control systems can be broadly classified into two categories: 
• Government-run systems, where the government bears most or all of the costs and controls the system to a significant extent.
• Private insurance markets, where costs are allocated and care is provided by private insurance companies.
• For individuals, policyholders pay ongoing premiums and may increase due to general increases in health care cost and age of the policyholder similar to life insurance.
• For organizations, health insurance premiums resemble life insurance premiums when changes to the company's assessment of the risk of a payout do not lead to an increase in premiums.
• In some cases, insurance coverage may be denied to individuals which may be for certain period on new policy with preexisting medical conditions. Though it could cover if the preexisting medical conditions are unknown.

Mortality Table

• Mortality tables show the rate of death within a specific population. 
• Mortality tables utilize various factors to predict the likelihood of an individual’s death in the current year.
• Mortality tables are used heavily by insurance companies to value life insurance contracts and project future insured events.
• Please find below the sample mortality table, this would differ year to year and based on the particular region or other much more finer variables.

Credits: https://qsstudy.com/wp-content/uploads/2018/12/Mortality-Table.jpg

• A mortality table displays the likelihood of a person’s death before their next birthday based on age, life expectancy, and population survivorship of a population at varying ages. Please note the following details about the table below. 
• The first column displays the exact age assumed for the calculations present in the other columns. For example the last row the exact age is 83yrs.
• The second column shows the probability of dying within the next year. For 83yr old man the probability within the next year is 0.081070 or 8.1070%.
• The third column indicates the probability of surviving. In this case the survival rate is 0.412334 or 41.2334%.
• The fourth column displays the remaining life expectancy. Here for 83yr old man the remaining life is approximately 6.72 more years as the value is 6.72000, which is on an average 89.72.
• The mortality rates are different between men and women.
• Expected payout
• The term "expected payout" refers to the anticipated amount of money that an insurance company expects to pay out in claims over a certain period. This is a crucial aspect of the insurance business, as it helps insurers assess the financial risks associated with providing coverage. Ideally the premium collected should match the expected payout. 
• Simple example to understand expected payout:
• Example: Auto Insurance
• Assumptions: 
• An insurance company offers auto insurance policies.
• The policies cover potential damages from accidents.
• The insurance period is one year.
• Expected Payout Calculation:
• Data Analysis:
• The insurance company analyzes historical data, accident rates, and other factors to estimate that, on average, they might need to pay $500,000 in claims over the next year for all policies.
• Expected Payout per Policy:
• If they have 1,000 policyholders, the expected payout per policy is $500,000 / 1,000 = $500.

• Premium Calculation:
• Costs and Profit Margin:
• The insurance company considers operational costs, administrative expenses, and a desired profit margin. Let's say these amount to $200 per policy.
• Premium Calculation:
• The insurance company sets the premium to cover expected payouts, costs, and profit. In this case, the premium might be $500 (expected payout) + $200 (expenses and profit) = $700 per policy.
• Comparison:
• The insurance company collects $700 from each policyholder.
• If all 1,000 policyholders renew their policies, the total premium collected is $700 * 1,000 = $700,000.
• Financial Impact:
• The insurance company aims to collect more in premiums than they expect to pay out in claims, ensuring they have funds to cover payouts, expenses, and make a profit.
• The key idea is to balance the premium collected with the expected payout to ensure the financial stability of the insurance company while providing coverage to policyholders.
• Present value
• The present value of expected payout is a way for insurance companies to make sure they have enough money set aside today to cover the anticipated costs of future claims, accounting for the fact that money has a time-based value.
• Insurance companies expect to pay out money in the future to cover claims. For example, if someone has a car insurance policy, the insurance company expects to pay for damages in case of an accident.
• Time-based value, the money today is generally more valuable than the same amount of money in the future. This is because money can be invested or earn interest over time.
• The present value is a way of figuring out how much future payouts are worth in today's terms, considering the time value of money.
• To calculate the present value, we use a process called "discounting." It's like adjusting the future money to reflect its current value.
• Example: If an insurance company expects to pay $1,000 in claims one year from now and the discount rate (interest rate) is 5%, the present value would be less than $1,000 because of the time value of money.
• Formula:
• PV= (1+r)nFV
• Here,
• PV is the present value. 
• FV is the future value (expected payout). 
• r is the discount rate
• n is the number of periods (time until the payout)
• Calculating present value helps insurers understand the current financial impact of future payouts. It helps them plan for and manage the funds needed to fulfil their obligations to policyholders.
• Premium payment
• A premium is the amount of money that an individual or business pays to an insurance company for coverage. The premium is typically paid on a regular basis, such as monthly or annually, and it ensures that the policyholder has insurance protection for a specific period. Let's go through a simple example to illustrate the concept of premium payment in insurance:
• Example: Auto Insurance Premium
• Scenario:
• Jane wants to insure her car, so she purchases an auto insurance policy.
• The insurance policy covers damages to her car in case of an accident.
• The policy has an annual premium payment.

• Details
• Annual Auto Insurance Premium: $800
• Explanation:
• Policy Purchase: Jane contacts an insurance company and purchases an auto insurance policy to protect her car.
• Premium Amount: The insurance company determines that the annual cost of providing coverage for Jane's car is $800.
• Payment Frequency: Jane chooses to pay her premium annually, so she will be billed $800 once a year.
• Payment Process: Jane may have different options for paying her premium. She can choose to pay it in a lump sum at the beginning of the policy term or set up monthly payments.
• Coverage Period: The $800 premium payment provides coverage for Jane's car for the entire year.
• Renewal: At the end of the policy term (one year), Jane will need to renew her insurance. The premium for the next year might be adjusted based on factors like changes in coverage, the value of the insured car, or the policyholder's driving history.
• Total Cost:
• If Jane chooses to pay annually, she will pay $800 at the start of the policy term.
• If she opts for monthly payments, the annual premium may be divided into 12 monthly installments (e.g., $800 / 12 = $66.67 per month).
• Premiums are crucial for the financial stability of insurance companies. They allow insurers to collect funds upfront, ensuring they have the resources to cover potential claims and operating expenses.
• A premium is the cost paid by a policyholder for insurance coverage. It's a financial arrangement that enables individuals and businesses to transfer the risk of potential losses to an insurance company in exchange for a predetermined payment. The specific premium amount can vary based on factors such as the type of coverage, the insured property or person, and the insurer's underwriting criteria.

• Calculating premium payment and expected payout for a policyholder, lets do that with an example:
• Problem Statement:
• If the interest rates for all maturities are given as 4% per annum (with semiannual compounding). Premiums are paid once a year at the beginning of the year. What is an insurance company's break-even premium for $100,000 of term life insurance for a man of average health aged 80?
• Solution:
• If the term insurance lasts one year, the expected payout is calculated as probability of death multiplied the insurance coverage. For a man aged 80, from the mortality table, it is calculated to be $5,373.9 and is shown as:
• Formula: Probability of death * Insurance coverage
• 0.053739 × 100,000 = $5,373.9

• Calculate the present value of the expected payout. If we assume the payout occurs at the middle point of the year, the present value of the payout is $5269.54
• Formula: PV= (1+r)nFV
• $5,373.9 * (1 / ((1 + 0.04)^0.5)) = $5269.54
• Here,
• 5,373.9 is the expected value
• 0.04 is the given in the problem statement as 4% per annum
• 0.5 is the number of periods, as this semiannual its considered as half of one year.

• So far we have seen if the term insurance of one year, but if the term insurance lasts longer than one year, what will be the expected payout considering the present value of the two years. Let's perform two-year calculation. 
• If we suppose the term insurance lasts two years, the expected payout in the first year is still $5,373.9. 
• Formula for expected payoff in 2nd year: 
• (1st year survival probability) * P(death in the second year) * Insurance coverage
• Here the 1st year survival probability can be calculated by 1 minus P(death in the first year)
• The probability that the policyholder dies during the second year is (1 − 0.053739)× 0.065873 = 0.06233. 
• The expected payout in the second year is then $6,233 and is calculated as 0.06233 × $100,000 = $6,233. 
• If we assume the payout occurs in the middle of the second year, the present value of the payout is $14,487, as calculated below.
• $6,233 * 1/((1+0.04)^1.5) = $5,876.883 # 0.5 * 3 terms = 1.5
• $6,233 * 0.942866= $5,876.88 #Simplified version
• To calculate the total present value of payouts, one sums the two years. In this two-year case, the present value of the expected payouts is $11,146.42 
• Formula: PV of 1year + PV of 2year
• $5269.54 + $5,876.88 = $11,146.42

• Premium payments, up to this point, the calculations have been on the nominal and present value of expected payouts should death occur. What about premium payment? The insurance company has to cover the expected payouts. In the example above, it is known that the first premium has no risk. The second payment depends upon whether the individual lives to age 81. 
• This probability is the change that the person does not die during the first year. In this example, the probability is 83.27%.
• Formula: Probability of Survival in the 1st. year = 1 - P(Death 1st year)
• 1 − 0.053739 = 0.946261
• If the premium is dollars per year, the present value of the premium payments is given by: X + 0.946261 * 1/((1 + 0.04)^1) = 0.90986X
• With the above equation, the calculation of the break-even annual premium is found simply by equating the present value of the expected premium payments to the present value of the expected payout. In this case, the equation (below) and associated answer is $17,155.
•  0.90986 * X = $11,146.42
• X = $11,146.42/ 0.90986
• X = $12,250.69

Risk Management

Major Risk Facing Insurance Companies

• Insufficient funds to satisfy policyholders's claims: The reserves held by the insurance companies to meet the payouts as required by the claims of policyholders may fall short of their estimation. This is the biggest risk faced by the insurance companies. This could be due to sudden surge of payouts in a short time (e.g. mortality risk and catastrophe risk) or payouts that continue for longer than expected (e.g. longevity risk).
• Poor return on investments: They mostly invest in corporate bonds and when defaults on corporate bonds increases, it  takes a toll on the profitability of the insurance company. Diversification of investments by industry sector and geography can help mitigate such loses.
• Liquidity risk: They face liquidity risk associated with their investments. For example illiquid bonds give higher yields but they cannot be readily converted into cash to meet high claims when they are not anticipated beforehand.
• Credit risk: Since insurance companies enter into transactions with banks and reinsurance companies, they are exposed to credit risk, if the counterparty default its obligations. 
• Operational and business risks: Similar to banks, insurance companies faces losses due to failure of systems and procedures or external events outside the company's control (e.g. computer failure or human error).
• Misprice their risk: Insurance companies operate on risk models. If their economists and statisticians misestimate their expected costs due to, for example, an unexpected natural disaster, the result could be bankruptcy.

Moral Hazard

• Moral hazard describes the risk to the insurance company that having insurance will lead the policyholder to act more recklessly than if the policyholder did not have insurance.
• This difference in behaviour increases the risks and rises the expected payouts of the insurance company.
• Methods to mitigate against moral hazard includes the below: 
• Deductibles: The policyholder is responsible for bearing the first part of any loss. For example policyholder is responsible for a fixed amount of the loss.
• Co-insurance provision: The insurance company pays a predetermined percentage (less than 100%) of losses in excess of the deductible. For example insurance company will only pay a fixed percentage of losses
• Policy limit: An upper limit to the payout is set by the insurance company. For example fixed maximum payouts.
• By aligning the interest of the policyholders more closely with those of the insurance company, moral hazard can be handled better, using the above methods.

Adverse Selection

• Adverse selection describes the situation where an insurer is unable to differentiate between a good risk and a bad risk as a result it offers the same price to everyone, thereby attracting more of the bad risks (e.g. careless drivers, sick individuals).
• Just like moral hazard, adverse selection increases the chances of claims overwhelming the insurer, something that can lead to insolvency.
• To reduce the impact of the problems created due to adverse selection, an insurance company tries to do greater due diligence such as physical examination, researching driving records and so on, about the policyholder before committing itself. Also performs ongoing due diligence for example updating driving reports and adjusting premiums to reflect changing risks.

Mortality Risk

• Mortality risk refers to the risk of policyholders dying earlier than expected could be due to illness or disease. 
• Mortality risk is higher usually during wars, epidemics, natural disasters which will cause many individuals to die sooner than expected.
• From the perspective of the insurance company, the risk of losses increases due to the earlier-than-expected life insurance payout. Usually mortality risk is higher term insurance policies.
• In contrast, increased mortality risk increases the profitability of annuity contracts because the policyholders end up receiving fewer scheduled payments.
• In calculating the impact of mortality risk, it is important to consider the age groups within the population that are most affected by an event.

Longevity Risk

• Longevity Risk refers to the risk of the policyholders living longer than expected could be due to healthy lifestyle.
• From the perspective of the insurance company, the risk of losses increases due to the longer-than-expected annuity payout period. Usually longevity risk is higher term annuity policies.
• In contrast, increased longevity will improve the profitability of life insurance contracts, because the insured will end up paying more and more premiums.
• To handle loss caused due to longevity, longevity derivative or longevity bonds can be acquired. 

Hedging mortality and longevity risk

• First let's understand what does hedging means, hedging is a financial strategy used to reduce or offset the risk of potential losses in investments. It involves taking actions or making investments that counterbalance the potential negative impact of adverse price movements in the market.
• In an insurance company, the risks associated with long-term payments and potential death benefits for annuity contracts are often balanced out by the risks present in their regular life insurance policies. 
• However, when the overall financial exposure of the insurance company is significant, they may choose to mitigate these risks by obtaining reinsurance.
• Reinsurance is a method used by insurance companies to transfer some risk to another insurer in exchange for a premium, which helps them to mitigate potential losses.
• Derivative contracts, here the insurance companies may enter into longevity derivative contracts that provide favourable payoffs when they are concerned about their exposure to longevity risk on annuity contracts.
 
• A typical derivative here is the longevity bond:
• A population is defined
• A coupon payable as a particular date is a function of the number of people still alive at that point
• For example on longevity derivative contracts, let's say a pension fund purchases a longevity derivative contract for a group of retirees, and the benchmark is set at an average lifespan of 85 years. If the actual average lifespan of the retirees covered by the contract exceeds 85 years, the financial institution (counterparty) pays the pension fund an agreed-upon amount. This payout helps the pension fund offset the increased costs associated with longer life expectancies.

Fund Management

Capital Requirements for Insurance Companies

• In U.S. capital requirements are determined by state regulators using risk-based capital standards determined by the National Association of Insurance Commissioners (NAIC). The NAIC is an organization consisting of the chief insurance regulatory officials from all 50 states.
• In the European Union, insurance companies are regulated centrally implying similar regulatory framework across all member countries, this framework known as Solvency I.
• No global capital requirements exist for insurance company and Solvency I did not consider investment risks, however Solvency II (upgraded) is the set of rules and regulations implemented in 2016. 
• Under Solvency II, there is requirements
• Solvency Capital Requirement - SCR, if the capital < SCR, warning is issued as the company must increase above the SCR.
• Minimum Capital Requirement - MCR, if the capital < MCR, business operations may become significantly restricted.
• MCR is usually 25% to 45% of SCR.
• SCR and MCR, telling how much the capital is required, are calculated based on the sum of charges for:
• investment risk (assets)
• credit risk (due to investments)
• market risk (due to investments)
• underwriting risk (liability)
• operation risk
• Property-casualty insurance company requires more capital, due to the potential catastrophic nature and amount of claims are higher.
• Life insurance risks are lesser to certain extent due to predictable longevity and mortality risks.

Guaranty System for Insurance Companies

• Guaranty system protect policyholders from an insurance company’s inability to pay claims due to insolvency.
• Guaranty system exists for both insurance companies and banks, in U.S.
• Insurance companies are regulated at state level, whereas banks are regulated at the federal level.
• Regulation of insurance companies at the state level faces some shortcomings as mentioned below.
• Regulations tend to vary across different states. 
• Some insurance companies trade derivatives in the same way as banks, but are not subject to the same regulations as banks which can lead to some serious issues. 
• Insurance companies are required to be members of the guaranty association in every state where they operate. If an insurance company becomes insolvent in a state, every insurance company operating in the state contributes an amount to the state guaranty fund depending on the premium income it collects. The guaranty fund’s purpose is to compensate policyholders of the insolvent company. However, there may be limits on the amount of claims and some delays in the settlement process.
• The Dodd–Frank Act of 2010 in the US resulted in the formation of Federal Insurance Office (FIO) which monitors the insurance industry and identifies gaps in regulation.

Pension

• Many companies provide insurance to employees in form of guaranteed income for their rest of the lives once they have retired. 
• Both the company and its employees make regular monthly contributions to the plan and the funds in the plan are invested to provide income for retires.

Defined benefit plan

• In a defined benefit plan, the benefits to be received by the employee are defined, here employee benefit known and employer contribution unknown.
• Explicitly state the amount of the pension that the employee will receive upon retirement.
• The pension to be received by the employee after retirement is defined by a plan. The pension is calculated by a formula which is based on the number of years of employment and the employee's salary.
• There is significant risk borne by the employer because it is obligated to fund the benefit to the employee at retirement, therefore when the present value of the pension obligation exceeds the market value of the pension, the employer has to cover the deficiency.
• The computation of the pension liability is highly sensitive to the discount rate used and generally must be equal to yield on AA rated bonds.
• Additionally some defined plans may include indexation of pension amounts to account for inflation. Also continued pension payments to the surviving spouse upon the death of a retired employee, where the payout may be same or less than what pensioner received.
• A defined contribution plan is based on one employee’s individual account.
• The responsibility of the defined benefit plans lies with the employer

Defined contribution plan

• In a defined contribution plan, the monthly contributions to be made by the employees and employers to the pension plan are defined, here employer benefit known and employee contribution unknown.
• Both the employee and employer contributions are invested in one or more investments selected by the employee.
• When employees retire, the final value of the contributions invested can be converted to a lifetime annuity or received as a lump sum.
• Here the employer simply obligated to make set of contribution and risk is solely borne by the employee.
• In a defined benefit plan is based on a pooled account for all employees, as all the contributions go into and all the payments come out of the one account.
• The responsibility of the performance of a defined contribution plan is left in the hands of the employee. 


Conclusion

We have covered the risks involved as the organization and individual when dealing with insurance and pension plans.

Though we wish we should never use the insurance, but it is always good be prepared for the worst case. And today investing in pension plan will reap benifits in future. 

Credits and References

• https://www.youtube.com/watch?v=HyWrJRT1rWk
• https://www.youtube.com/watch?v=00_DQF3KHxg
• GARP, Schweser and Bionic Turtle Notes
• https://www.investopedia.com/
• http://chat.openai.com/ #shout out to the examples helped in learning the concepts