Bond and Option Pricing, Portfolio Management, and Investment Analysis
Chapter 14: Bond Pricing
Callable bonds should offer higher promised yields to maturity to compensate investors for the fact that they will not realize full capital gains should the interest rate fall and the bonds be called away from them at the stipulated call price. Bonds often are issued with a period of call protection. In addition, discount bonds selling significantly below their call price offer implicit call protection. Put bonds give the bondholder rather than the issuer the option to terminate or extend the life of the bond. Convertible bonds may be exchanged, at the bondholder’s discretion, for a specified number of shares of stock. Convertible bondholders “pay” for this option by accepting a lower coupon rate on the security. Floating-rate bonds pay a coupon rate at a fixed premium over a reference short-term interest rate. Risk is limited because the rate is tied to current market conditions. Collateralized debt obligations are used to reallocate the credit risk of a pool of loans. The pool is sliced into tranches, with each tranche assigned a different level of seniority in terms of its claims on the cash flows from the underlying loans. High seniority tranches are usually quite safe, with credit risk concentrated on the lower level tranches. Each tranche can be sold as a stand-alone security.
The current yield on a bond is equal to annual interest payment divided by the current market price. Current yield is a measure of the income generated by a bond, expressed as a percentage of its current market price. It is calculated by dividing the annual interest payment by the current market price of the bond. To earn a high rating from the bond rating agencies, a firm should have a low debt to equity ratio and a high quick ratio. Ceteris paribus, the price and yield on a bond are negatively related. The relationship between bond price and yield is inversely related, meaning that when one increases, the other decreases, and vice versa. This relationship is known as the bond price-yield relationship or the price-yield curve. As bond prices increase, yields decrease, and as bond prices decrease, yields increase. A coupon bond is a bond that pays interest on a regular basis (typically every six months). Coupon bonds are characterized by periodic interest payments, known as coupon payments, typically made semi-annually, annually, or quarterly, depending on the terms of the bond. The coupon rate is the fixed interest rate applied to the bond’s face value, and it determines the amount of each coupon payment.
Consider two bonds, X and Y. Both bonds presently are selling at their par value of $1,000. Each pays interest of $150 annually. Bond X will mature in 6 years while bond Y will mature in 7 years. If the yields to maturity on the two bonds decrease from 15% to 12% both bonds will increase in value, but bond Y will increase more than bond X. It is a general property that, ceteris paribus, the prices of bonds with longer maturities change more as required yields change. since bond Y has a longer maturity, it will experience a larger price increase due to the decrease in yield to maturity. Consider a 5-year bond with a 10% coupon that has a present yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be lower. If interest rates remain constant, one year from now the price of this bond will be lower. The bonds is currently selling at a premium to par. To prevent arbitrage, the bond must sell at par when it matures. Thus, each year, the premium decreases (price declines toward par). Which one of the following statements about convertibles is true? The more volatile the underlying stock, the greater the value of the conversion feature. This is because the probability of profitable conversion increases. When the underlying stock is more volatile, there is a higher likelihood of significant fluctuations in its price. This volatility increases the potential upside for bondholders who can convert their bonds into shares of the stock, thereby capturing any price increases. As a result, the conversion feature becomes more valuable when the underlying stock is more volatile.
When a bond indenture includes a sinking fund provision bondholders may lose because their bonds can be repurchased by the corporation at below-market prices. When a bond indenture includes a sinking fund provision bondholders may lose because their bonds can be repurchased by the corporation at below-market prices. One year ago, you purchased a newly issued TIPS bond that has a 6% coupon rate, five years to maturity, and a par value of $1,000. The average inflation rate over the year was 4.2%. What is the amount of the coupon payment you will receive and what is the current face value of the bond? The bond price, which is indexed to the inflation rate, becomes $1,000 × 1.042 = $1,042. The interest payment is based on the coupon rate and the new face value. The interest amount equals $1,042 × .06 = $62.52. Bond analysts might be more interested in a bond’s yield to call if interest rates are expected to fall. Bond analysts might be more interested in a bond’s yield to call if interest rates are expected to fall. If rates fall, firms may desire to call higher coupon bonds. CFA.5.C: The advantage of a callable bond is the higher coupon (and higher promised yield to maturity) when the bond is issued. If the bond is never called, then an investor earns a higher realized compound yield on a callable bond issued at par than a noncallable bond issued at par on the same date. The disadvantage of the callable bond is the risk of call. If rates fall and the bond is called, then the investor receives the call price and then has to reinvest the proceeds at interest rates that are lower than the yield to maturity at which the bond originally was issued. In this event, the firm’s savings in interest payments is the investor’s loss. CFA.2: Current yield = Coupon/Price . YTM = 3.993% semi-annually, or 7.986% annual bond equivalent yield. On a financial calculator, enter: n = 10; PV = –960; FV = 1000; PMT = 35 Compute the interest rate. ealized compound yield is 4.166% (semi-annually), or 8.332% annual bond equivalent yield. To obtain this value, first find the future value (FV) of reinvested coupons and principal. There will be six payments of $35 each, reinvested semi-annually at 3% per period. On a financial calculator, enter: PV = 0; PMT = 35; n = 6; i = 3%. Compute: FV = 226.39 Three years from now, the bond will be selling at the par value of $1,000 because the yield to maturity is forecast to equal the coupon rate. Therefore, total proceeds in three years will be: $226
.39 + $1,000 = $1,226.39. Alternatively, PV = −$960; FV = $1,226.39; N = 6; PMT = $0. Solve for I = 4.166%. 14.25: Factors that might make the ABC debt more attractive to investors, therefore justifying a lower coupon rate and yield to maturity, are: i. The ABC debt is a larger issue and therefore may sell with greater liquidity. ii. An option to extend the term from 10 years to 20 years is favorable if interest rates 10 years from now are lower than today’s interest rates. In contrast, if interest rates increase, the investor can present the bond for payment and reinvest the money for a higher return. iii. In the event of trouble, the ABC debt is a more senior claim. It has more underlying security in the form of a first claim against real property. iv. The call feature on the XYZ bonds makes the ABC bonds relatively more attractive. since ABC bonds cannot be called from the investor. v. The XYZ bond has a sinking fund requiring XYZ to retire part of the issue.
CH15: The forward rate of interest is the break-even future interest rate that would equate the total return from a rollover strategy to that of a longer-term zero-coupon bond. It is defined by the equation, where n is a given number of periods from today. The yield curve shows at any point in time the relationship between yield on a bond and the time to maturity on the bond. The yield curve is a graphical representation of the yields (interest rates) of bonds with different maturities at a specific point in time. It shows the relationship between the yield (interest rate) and the time to maturity of bonds. Typically, the yield curve slopes upward, indicating that longer-term bonds have higher yields than shorter-term bonds. This relationship is crucial for understanding the term structure of interest rates and market expectations. According to the expectations hypothesis, an upward sloping yield curve implies that interest rates are expected to increase in the future. The expectations hypothesis suggests that the shape of the yield curve reflects investors’ expectations about future interest rates.An upward-sloping yield curve indicates that longer-term interest rates are higher than shorter-term interest rates. This implies that investors expect interest rates to increase in the future. Otherwise, they would not demand higher yields for longer-term bonds. According to the “liquidity preference” theory of the term structure of interest rates, the yield curve usually should be normal or upward sloping. When computing yield to maturity, the implicit reinvestment assumption is that the interest payments are reinvested at the yield to maturity at the time of the investment. the implicit reinvestment assumption is that the interest payments are reinvested at the yield to maturity at the time of the investment. Forward rates differ from future short rates because they are imperfect forecasts. Forward rates represent the expected future interest rates at a specific point in time. These rates are estimated based on current market conditions and expectations of future economic factors. Future short rates, on the other hand, are the actual short-term interest rates that will prevail in the future. They are not forecasts but rather outcomes that will be realized at a later date. Treasury STRIPS are created by selling each coupon or principal payment from a whole Treasury bond as a separate cash flow. If the value of a Treasury bond was lower than the value of the sum of its part (STRIPPED cash flows) you could not profit by buying the stripped cash flows and reconstituting the bond OR profit by buying the bond and creating STRIPS. The pure yield curve can be estimated by using zero-coupon Treasuries OR by using stripped Treasuries if each coupon is treated as a separate “zero.” ______ can occur if _____. Arbitrage (also known as riskless economic profit) can occur if the Law of One Price is violated. The yield curve is a component of the index of leading economic indicators. Since the yield curve is often used to forecast the business cycle, it is used as one of the leading economic indicators. 15.1: n general, the forward rate can be viewed as the sum of the market’s expectation of the future short rate plus a potential risk (or liquidity) premium. According to the expectations theory of the term structure of interest rates, the liquidity premium is zero so that the forward rate is equal to the market’s expectation of the future short rate. Therefore, the market’s expectation of future short rates (i.e., forward rates) can be derived from the yield curve, and there is no risk premium for longer maturities. The liquidity preference theory, on the other hand, specifies that the liquidity premium is positive so that the forward rate is greater than the market’s expectation of the future short rate. This could result in an upward sloping term structure even if the market does not anticipate an increase in interest rates. The liquidity preference theory assumes that the financial markets are dominated by short-term investors who demand a premium in order to be induced to invest in long maturity securities. 15.6: The yield curve slopes upward because short-term rates are lower than long-term rates. Since market rates are determined by supply and demand, it follows that investors (on the demand side) expect rates to be higher in the future than in the near-term.
CH16: Even default-free bonds such as Treasury issues are subject to interest rate risk. Longer-term bonds generally are more sensitive to interest rate shifts than are short-term bonds. A measure of the average life of a bond is Macaulay’s duration, defined as the weighted average of the times until each payment made by the security, with weights proportional to the present value of the payment. Duration is a direct measure of the sensitivity of a bond’s price to a change in its yield. The proportional change in a bond’s price equals the negative of duration multiplied by the proportional change in 1 + y. Immunization strategies are characteristic of passive fixed-income portfolio management. Such strategies attempt to render the individual or firm immune from movements in interest rates. This may take the form of immunizing net worth or, instead, immunizing the future accumulated value of a fixed-income portfolio. The duration of a bond is a function of the bond’s coupon rate. Time to maturity. Yield to maturity. Duration is calculated by discounting the bond’s cash flows at the bond’s yield to maturity and, except for zero-coupon bonds, is always less than time to maturity. The “modified duration” used by practitioners is equal to the Macaulay duration The “modified duration” used by practitioners is equal to the Macaulay duration divided by (one plus the bond’s yield to maturity). D* = D/(1 + y). The interest-rate risk of a bond is the risk that arises from the uncertainty of the bond’s return caused by changes in interest rates. The interest-rate risk of a bond is the risk that arises from the uncertainty of the bond’s return caused by changes in interest rates. Changing interest rates change the bond’s return, both in terms of the price of the bond and the reinvestment of coupon payments. Which of the following two bonds is more price sensitive to changes in interest rates? A par value bond, X, with 10 years-to-maturity and a 10% coupon rate or a zero-coupon bond, Y, with 10 years-to-maturity and a 10% yield-to-maturity. Bond Y because of the longer duration. Bond Y is more sensitive because it has a longer duration. Holding other factors constant, which one of the following bonds has the smallest price volatility? 6 year, 15% coupon bond. The bond has the smallest price volatility would be the 6 year, 15% coupon bond since it has the shortest duration. Which of the following is not true? Given time to maturity, the duration of a zero-coupon decreases with yield to maturity. Duration is directly related to time to maturity, inversely related to coupon rate, and is a better measure of price sensitivity to interest rate changes than is time to maturity. However, given time to maturity, the duration of a zero-coupon increases with yield to maturity. Par value bond GE has a modified duration of 11. Which one of the following statements regarding the bond is true? If the market yield increases by 1%, the bond’s price will decrease by $110. δP/P = -D*δy; -$110 = -11(0.01) × $1,000. Indexing of bond portfolios is difficult because the number of bonds included in the major indexes is so large that it would be difficult to purchase them in the proper proportions. many bonds are thinly traded so it is difficult to purchase them at a fair market price. the composition of bond indexes is constantly changing. A substitution swap is an exchange of bonds undertaken to profit from apparent mispricing between two bonds. A substitution swap is an example of bond price arbitrage, undertaken when the portfolio manager attempts to profit from apparent mispricing. An analyst who selects a particular holding period and predicts the yield curve at the end of that holding period is engaging in horizon analysis. Horizon analysis involves selecting a particular holding period and predicting the yield curve at the end of that holding period. The holding period return for the bond can then be predicted.
CH17: Macroeconomic policy aims to maintain the economy near full employment without aggravating inflationary pressures. The proper trade-off between these two goals is a source of ongoing debate. The most widely used monetary tool is open market operations. Monetary policy is determined by the board of Governors of the Federal Reserve System. Fiscal policy is difficult to implement quickly because it requires political negotiations and much of government spending is non-discretionary and cannot be changed. Supply-side economists wishing to stimulate the economy are most likely to recommend a decrease in the tax rate. The process of estimating the dividends and earnings that can be expected from the firm based on determinants of value is called fundamental analysis.. During which stage of the industry life cycle would a firm experience stable growth in sales? Consolidation. One of the features of the Consolidation phase is stable growth. There is no “Stabilization” stage. During start-up there is rapid growth; during the maturity phase there is slowing growth; and during the relative decline phase there is minimal or negative growth. If interest rates decrease, business investment expenditures are likely to ______ and consumer durable expenditures are likely to _________. If interest rates decrease, business investment expenditures are likely to increase and consumer durable expenditures are likely to increase. If the economy is growing, firms with low operating leverage will experience smaller increases in profits than firms with high operating leverage. According to Michael Porter, there are five determinants of competition. An example of Pressure from substitute products is when the availability of similar products in related industries limits the prices that can be charged to customers. A top down analysis of a firm starts with The global economy.
CH18: One approach to firm valuation is to focus on the firm’s book value, either as it appears on the balance sheet or as adjusted to reflect current replacement cost of assets or liquidation value. Another approach is to focus on the present value of expected future dividends. The dividend discount model holds that the price of a share of stock should equal the present value of all future dividends per share, discounted at an interest rate commensurate with the risk of the stock. The constant-growth version of the DDM asserts that if dividends are expected to grow at a constant rate forever, the intrinsic value of the stock is determined by the formula Vo = D1/k-g g = ROE *(1=Dividen payout). Many analysts form their estimates of a stock’s value by multiplying their forecast of next year’s EPS by a predicted P/E multiple. Some analysts mix the P/E approach with the dividend discount model. They use an earnings multiplier to forecast the terminal value of shares at a future date, and add the present value of that terminal value with the present value of all interim dividend payments. Liquidation value per share is the amount of money per common share that could be realized by breaking up the firm, selling the assets, repaying the debt, and distributing the remainder to shareholders. A company has an expected ROE of 11%. The dividend growth rate will be 8.25% if the firm follows a policy of paying 25% of earnings in the form of dividends. 11% x 0.75 = 8.25%.. One of the problems with attempting to forecast stock market values is that the level of uncertainty surrounding the forecast will always be quite high. Historically, P/E ratios have tended to be lower when inflation has been high. A preferred stock will pay a dividend of $2.50 in the upcoming year, and every year thereafter, i.e., dividends are not expected to grow. You require a return of 10% on this stock. Use the constant growth DDM to calculate the intrinsic value of this preferred stock. $2.50 / 0.10 = $25.00. If a firm has a required rate of return equal to the ROE the amount of earnings retained by the firm does not affect market price or the P/E. The goal of fundamental analysts is to find securities whose intrinsic value exceeds market price. Many stock analysts assume that a mispriced stock will gradually approach its intrinsic value over several years. Because the DDM requires multiple estimates, investors should carefully examine inputs to the model, and perform sensitivity analysis on price estimates.
CH19: To create a common size income statement divide all items on the income statement by total revenue. An example of a liquidity ratio is the current ratio and the acid test or quick ratio. A firm has a higher asset turnover ratio than the industry average, which implies the firm is utilizing assets more efficiently than other firms in the industry. A measure of asset utilization is return on total assets.. During periods of inflation, the use of FIFO (rather than LIFO) as the method of accounting for inventories causes higher income taxes. MBC Company has a ratio of (total debt/total assets) that is above the industry average, and a ratio of (long term debt/equity) that is below the industry average. These ratios suggest that the firm has relatively high current liabilities. Which of the following ratios gives information on the amount of profits reinvested in the firm over the years? Retained earnings/total assets gives information on the amount of profits reinvested in the firm over the years Comparability problems arise because firms may use different generally accepted accounting principles, and inflation may affect firms differently due to accounting conventions used.
CH20: American-style options allow exercise on or before the expiration date. European options allow exercise only on the expiration date. Most traded options are American in nature. Options are traded on stocks, stock indexes, foreign currencies, fixed-income securities, and several futures contracts.. The put-call parity theorem relates the prices of put and call options. If the relationship is violated, arbitrage opportunities will result. Specifically, the relationship that must be satisfied is: Many commonly traded securities embody option characteristics. Examples of these securities are callable bonds, convertible bonds, and warrants. Other arrangements such as collateralized loans and limited-liability borrowing can be analyzed as conveying implicit options to one or more parties.. A European put option allows the holder to potentially benefit from a stock price decrease with less risk than short selling the stock and to sell the underlying asset at the striking price on the expiration date. An American call option allows the buyer to buy the underlying asset at the exercise price on or before the expiration date and to sell the option in the open market prior to expiration. The maximum loss a buyer of a stock call option can suffer is equal to the call premium. The intrinsic value of an out-of-the-money call option is equal to zero. Only in-the-money options have a positive intrinsic value. The maximum loss the writer of a stock put option can suffer is equal to the striking price minus the put premium. According to the put-call parity theorem, the value of a European put option on a non-dividend paying stock is equal to the call value plus the present value of the exercise price minus the stock price. Before expiration, the time value of a call option is equal to the actual call price minus the intrinsic value of the call. The value of a stock put option is positively related to the factors listed except the stock price. The put-call parity theorem allows for arbitrage opportunities if violated, represents the proper relationship between put and call prices, and may be violated by small amounts, but not enough to earn arbitrage profits, once transaction costs are considered A callable bond should be priced the same as a straight bond plus a call option
CH21: Option values may be viewed as the sum of intrinsic value plus time or “volatility” value. The volatility value is the right to choose not to exercise if the stock price moves against the holder. Thus the option holder cannot lose more than the cost of the option regardless of stock price performance. Call options are more valuable when the exercise price is lower, when the stock price is higher, when the interest rate is higher, when the time to expiration is greater, when the stock’s volatility is greater, and when dividends are lower. Call options must sell for at least the stock price less the present value of the exercise price and dividends to be paid before expiration. This implies that a call option on a non-dividend-paying stock may be sold for more than the proceeds from immediate exercise. Thus European calls are worth as much as American calls on stocks that pay no dividends, because the right to exercise the American call early has no value. European put values can be derived from the call value and the put-call parity relationship. This technique cannot be applied to American puts for which early exercise is a possibility. he implied volatility of an option is the standard deviation of stock returns consistent with an option’s market price. It can be backed out of an option-pricing model by finding the stock volatility that makes the option’s value equal to its observed price. Portfolio A consists of 150 shares of stock and 300 calls on that stock. Portfolio B consists of 575 shares of stock. The call delta is 0.7. Which portfolio has a higher dollar exposure to a change in stock price? 300 calls (0.7) = 210 shares + 150 shares = 360 shares; 575 shares = 575 shares. Portfolio B A portfolio consists of 100 shares of stock and 1500 calls on that stock. If the hedge ratio for the call is 0.7, what would be the dollar change in the value of the portfolio in response to a one dollar decline in the stock price? -$100 + [-$1,500(0.7)] = -$1,150 The Black-Scholes formula assumes that: the risk-free interest rate is constant over the life of the option. the stock price volatility is constant over the life of the option. there will be no sudden extreme jumps in stock prices. The dollar change in the value of a stock call option is always lower than the dollar change in the value of the stock. The elasticity of a stock call option is always greater than one. Option prices are much more volatile than stock prices, as option premiums are much lower than stock prices. A put option on the S&P 500 index will best protect a portfolio that corresponds to the S&P 500. The dividend yield of underlying stock, time to expiration of the option, the level of interest rates, and stock price volatility influence the value of options The gamma of an option is the sensitivity of the delta to the stock pric If the company unexpectedly announces it will pay its first-ever dividend 3 months from today, you would expect that the call price would decrease.As an approximation, subtract the present value of the dividend from the stock price and recompute the Black-Scholes value with this adjusted stock price. Since the stock price is lower, the option value will be lower. In volatile markets, dynamic hedging may be difficult to implement because prices move too quickly for effective rebalancing, as volatility increases, historical deltas are too low, price quotes may be delayed so that correct hedge ratios cannot be computed, and volatile markets may cause trading halts.
CH24: Sharpe: when the portfolio represents the entire investment fund. nformation ratio: when the portfolio represents the active portfolio to be optimally mixed with the passive portfolio. Treynor or Jensen: when the portfolio represents one subportfolio of many. Many observations are required to eliminate the effect of the “luck of the draw” from the evaluation process because portfolio returns commonly are very “noisy. The shifting mean and variance of actively managed portfolios make it even harder to assess performance. A typical example is the attempt of portfolio managers to time the market, resulting in ever-changing portfolio betas. Style analysis uses a multiple regression model where the factors are category (style) portfolios such as bills, bonds, and stocks. A regression of fund returns on the style portfolio returns generates residuals that represent the value added of stock selection in each period. These residuals can be used to gauge fund performance relative to similar-style funds Common attribution procedures partition performance improvements to asset allocation, sector selection, and security selection. Performance is assessed by calculating departures of portfolio composition from a benchmark or neutral portfolio. Most professionally managed equity funds generally underperform the S&P 500 index on both raw and risk-adjusted return measures. A pension fund that begins with $500,000 earns (and pays out) 15% the first year and 10% the second year. At the beginning of the second year, the sponsor contributes another $300,000. The dollar-weighted and time-weighted rates of return, respectively, were 12.1% and 12.5%. $500,000 + $300,000/(1 + r) = $75,000/(1 + r) + $880,000/(1 + r)2; r = 12.059%; (15 + 10)/2 = 12.5% The Sharpe, Treynor, and Jensen portfolio performance measures are derived from the CAPM, however, the Sharpe and Treynor measures use different risk measures; therefore the measures vary as to whether or not they are appropriate, depending on the investment scenario. Suppose the risk-free return is 3%. The beta of a managed portfolio is 1.75, the alpha is 0%, and the average return is 16%. Based on Jensen’s measure of portfolio performance, you would calculate the return on the market portfolio as 10.4%. 0% = 16% – [3% + 1.75(x – 3%)]; x = 10.4% Suppose you own two stocks, A and B. In year 1, stock A earns a 2% return and stock B earns a 9% return. In year 2, stock A earns an 18% return and stock B earns an 11% return. The two stocks have the same arithmetic average return. Stock A’s average return is (2 + 18)/2 = 10%. Stock B’s average return is (9 + 11)/2 = 10% Suppose two portfolios have the same average return, the same standard deviation of returns, but portfolio X has a higher beta than portfolio Y. According to the Sharpe measure, the performance of portfolio X. According to the Sharpe measure, the performance of portfolio X is the same as the performance of portfolio Y. The Sharpe measure measures the reward to volatility trade-off by dividing the average portfolio excess return by the standard deviation of returns The Jensen portfolio evaluation measure is an absolute measure of return over and above that predicted by the CAPM. The M-squared measure considers the risk-adjusted return when evaluating mutual funds A portfolio manager’s ranking within a comparison universe may not provide a good measure of performance because portfolio durations can vary across managers. AND if managers follow a particular style or subgroup, portfolios may not be comparable. Returns are typically time-weighted for all portfolios and broad risk classes or styles are grouped together, but particular subgroups and differences in duration are typically not considered People living on money-fixed incomes are vulnerable to inflation risk and may want to hedge against it. The effectiveness of an asset as an inflation hedge is related to its correlation with unanticipated inflation. For investors who must pay taxes on their investment income, the process of asset allocation is complicated by the fact that they pay income taxes only on certain kinds of investment income. Interest income on munis is exempt from tax, and high-tax-bracket investors will prefer to hold them rather than short- and long-term taxable bonds. However, the really difficult part of the tax effect to deal with is the fact that capital gains are taxable only if realized through the sale of an asset during the holding period. Investment strategies designed to avoid taxes may conflict with the principles of efficient diversification. he life cycle approach to the management of an individual’s investment portfolio views the individual as passing through a series of stages, becoming more risk averse in later years. The rationale underlying this approach is that as we age, we use up our human capital and have less time remaining to recoup possible portfolio losses through increased labor supply. Investment policies refer to strategies aimed at attaining the established rate of return requirements while meeting expressed risk tolerance and applicable constraints. An important benefit of Keogh plans is that they are not taxable until funds are withdrawn as benefits. The prudent investor law requires professional investors who manage money for others to constrain their investments to those that would have been approved by the prudent investor. A remainderman is one who receives the principal of a trust when it is dissolved. The first step a pension fund should take before beginning to invest is to establish investment objectives. Suppose that the pre-tax holding period returns on two stocks are the same. Stock X has a high dividend payout policy and stock Y has a low dividend payout policy. If you are an individual in a high marginal tax bracket and do not intend to sell the stocks during the holding period, Stock Y will have a higher after-tax holding period return than stock X because less taxes were required to be paid on the dividends distributions. Investors seeking to diversify are likely to find that their largest investment is in their job.