CFA Questioins:Chapter: Problem:

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CFA Examination III (1993)

9(a). At this point we know (or can reasonably infer) that Mr. Franklin is:

unmarried (a recent widower)

childless

70 years of age

in good health

possessed of a large amount of (relatively) liquid wealth intending to leave his estate to a tax-exempt medical research foundation, to whom he is also giving a large current cash gift

free of debt (not explicitly stated, but neither is the opposite)

in the highest tax brackets (not explicitly stated, but apparent)

not skilled in the management of a large investment portfolio, but also not a complete novice since he owned significant assets of his own prior to his wife's death

not burdened by large or specific needs for current income

not in need of large or specific amounts of current liquidity

Taking this knowledge into account, his Investment Policy Statement will reflect these specifics:

Objectives:

Return Requirements: The incidental throw-off of income from Mr. Franklin's large asset pool should provide a more than sufficient flow of net spendable income. If not, such a need can easily be met by minor portfolio adjustments. Thus, an inflation-adjusted enhancement of the capital base for the benefit of the foundation will be the primary return goal (i.e., real growth of capital). Tax minimization will be a continuing collateral goal.

Risk Tolerance: A ccount c ircumstances and the long-term return goal suggest t hat the portfolio can take somewhat above average risk. Mr. Franklin is acquainted with the nature of investment risk from his prior ownership of stocks and bonds, he has a still long actuarial life expectancy and is in good current health, and his heir - the foundation, thanks to his generosity - is already possessed of a large asset base.

Constraints:

Time Horizon: Even disregarding Mr. Franklin's still-long actuarial life expectancy, the horizon is long-term because the remainder of his estate, the foundation, has a virtually perpetual life span.

Liquidity Requirement: Given what we know and the expectation of an ongoing income stream of considerable size, no liquidity needs that would require specific funding appear to exist.

Taxes: Mr. Franklin is no doubt in the highest tax brackets, and investment actions should take that fact into account on a continuing basis. Appropriate tax-sheltered investment (standing on their own merits as investments) should be considered. Tax minimization will be a specific investment goal.

Legal and Regulatory: Investments, if under the supervision of an investment management firm (i.e., not managed by Mr. Franklin himself) will be governed by state law and the Prudent Person rule.

Unique Circumstances: The large asset total, the foundation as their ultimate recipient, and the great freedom of action enjoyed in this situation (i.e., freedom from confining considerations) are important in this situation, if not necessarily unique.

9(b). Given that stocks have provided (and are expected to continue to provide) higher risk-adjusted returns than either bonds or cash, and considering that the return goal is for long-term, inflation-protected growth of the capital base, stocks will be allotted the majority position in the portfolio. This is also consistent with Mr. Franklin's absence of either specific current income needs (the ongoing cash flow should provide an adequate level for current spending) or specific liquidity needs. It is likely that income will accumulate to some extent and, if so, will automatically build a liquid emergency fund for Mr. Franklin as time passes.

Since the inherited warehouse and the personal residence are significant (15%) real estate assets already owned by Mr. Franklin, no further allocation to this asset class is made. It should be noted that the warehouse is a source of cash flow, a diversifying asset and, probably, a modest inflation hedge. For tax reasons, Mr. Franklin may wish to consider putting some debt on this asset, freeing additional cash for alternative investment use.

Given the long-term orientation and the above-average risk tolerance in this situation, about 70% of total assets can be allocated to equities (including real estate) and about 30% to fixed income assets. International securities will be included in both areas, primarily for their diversification benefits. Municipal bonds will be included in the fixed income area to minimize income taxes. There is no need to press for yield in this situation, nor any need to deliberately downgrade the quality of the issues utilized. Venture capital investment can be considered, but any commitment to this (or other "alternative" assets) should be kept small.

The following is one example of an appropriate allocation that is consistent with the Investment Policy Statement and consistent with the historical and expected return and other characteristics of the various available asset classes:

Range (%)Current

Target (%)

Cash/Money Market0 - 50

U.S. Fixed Income10 2015

Non-U.S. Fixed Income5 1510

U.S. Stocks (Large Cap)30 4530

(Small Cap)15 2515

Non-U.S. Stocks15 2515

Real Estate10 1515*

Other0 50

100

An alternate allocation could well be weighted more heavily to U.S. fixed income and less so to U.S. stocks, given the near equality of expected returns from those assets as indicated in Table 4.Given the long-term orientation and the above-average risk tolerance in this situation, about 70% of total assets can be allocated to equities (including real estate) and about 30% to fixed income assets. International securities will be included in both areas, primarily for their diversification benefits. Municipal bonds will be included in the fixed income area to minimize income taxes. There is no need to press for yield in this situation, nor any need to deliberately downgrade the quality of the issues utilized. Venture capital investment can be considered, but any commitment to this (or other "alternative" assets) should be kept small.The following is one example of an appropriate allocation that is consistent with the Investment Policy Statement and consistent with the historical and expected return and other characteristics of the various available asset classes:Range (%)Current

Target (%)

Cash/Money Market0 - 50

U.S. Fixed Income10 2015

Non-U.S. Fixed Income5 1510

U.S. Stocks (Large Cap)30 4530

(Small Cap)15 2515

Non-U.S. Stocks15 2515

Real Estate10 -1515*

Other0 50

100

*Includes the Franklin residence and warehouse, which together comprise the proportion of total assets shown.

26. CFA Examination II (1993)

26(a). The fundamental impact of the Fama and French research is to challenge the validity of the Capital Asset Pricing Model (CAPM). Specifically, they found little relation between beta and average stock returns over the 50-year period 1941-1990 (although there were some sub-periods when a positive relationship was indicated).

To isolate the "pure" impact of beta, Fama and French evaluated the joint roles of beta, size, earnings/price, leverage, and book-to-market over a broad range of large and small-capitalization stocks from 1963-1990. They found no relation between beta and average return over this period; on the other hand, a combination of book-to-market and size factors did explain differences in those average returns.

Max's attractive results for his low price/cash flow strategy might have arisen from (1) a bias toward small stocks-as a result of equal-weighting the stocks in the portfolio - and (2) a value bias, which might more realistically be reflecting low price/book relationships.

If asset pricing is rational and the Fama and French research is valid, performance (i.e., returns) should be evaluated by comparing average returns for a portfolio to a benchmark comprised of similar size and book-to-market characteristics, not by reference to beta.

Also, Abel points out that an extension to the CAPM, the consumption CAPM, predicts a much lower equity risk premium compare to what has actually occurred. This suggests that the predictive ability of CAPM, and hence the validity of beta, is questionable.

26(b). Many studies have been done on single-factor models, including such factors as size, price/earnings, beta, "neglect," day-of-the-week, etc., all of which have been referred to as "naive" anomalies. Often, the results have been taken as strong evidence of market inefficiencies and the opportunity to create attractive investment management products. However, these simple variable effects are not independent; rather there may be a complex web of interrelationships underlying a host of different variables.

As computer power has become more available and databases more extensive, researches have been able to test several variables simultaneously, rather than just one variable in isolation, often using a multiple regression framework. Using such techniques, they have been able to disentangle the observed effects and to isolate the "pure" and independent impacts of each variable. Jacobs and Levy, for example, studied a total of 25 separate anomaly measures, together with industry effects, and did so simultaneously.

As a single-factor study, Max's price/cash flow results merely indicate a naive anomaly, one that may simply b e a proxy for other, more significant underlying factors. To make them credible would require further research using a more robust model design to see if the results hold up. An example of a similar situation is found in the Jacobs and Levy work, where a simple price/cash flow screen is found to produce an illusory anomaly: its naive results were completely dissipated in the pure form test.

26(c). A number of problems exist with respect to Max's test design including:

1. Survivorship Bias - Max used the current list of S&P 500 Index companies rather than the list as it existed at the start of each test year. Thus, he failed to account for companies that may have left the list during the backtest period due to bankruptcy (affecting his negative returns) or that may have been merged out of existence (affecting his positive returns).

2. Look-Ahead Bias - It is not clear that Max used only that information that was available to all investors at the time that the ranking process implied it was. For example, a company's 1983 cash flow would not have been known until many weeks or several months after the end of 1983, not at actual year end when price data was available.

4. Beta is easily rolled over. Richard Roll has demonstrated that by changing the market index against which betas are measured, one can obtain quite different measures of the risk level of individual stocks and portfolios. As a result, one would make different predictions about the expected returns, and by changing indexes, one could change the risk-adjusted performance ranking of a manager.

CFA Examination II (1994)

15(a). The concepts are explained as follows:

The Foundation's portfolio currently holds a number of securities from two asset classes. Each of the individual securities has its own risk (and return) characteristics, described as specific risk. By including a sufficiently large number of holdings, the specific risk of the individual holdings offset each other, diversifying away much of the overall specific risk and leaving mostly nondiversifiable or market-related risk.

Systematic risk is market-related risk that cannot be diversified away. Because systematic risk cannot be diversified away, investors are rewarded for assuming this risk.

The variance of an individual security is the sum of the probability-weighted average of the squared differences between the security's expected return and its possible returns. The standard deviation is the square root of the variance. Both variance and standard deviation measure total risk, including both systematic and specific risk. Assuming the rates of return are normally distributed, the likelihood for a range of rates may be expressed using standard deviations. For example, 68 percent of returns may be expressed using standard deviations. Thus, 68 percent of returns can be expected to fall within + or -1 standard deviation of the mean, and 95 percent within 2 standard deviations of the mean.

Covariance measures the extent to which two securities tend to move, or not move, together. The level of covariance is heavily influenced by the degree of correlation between the securities (the correlation coefficient) as well as by each security's standard deviation. As long as the correlation coefficient is less than 1, the portfolio standard deviation is less than the weighted average of the individual securities' standard deviations. The lower the correlation, the lower the covariance and the greater the diversification benefits (negative correlations provide more diversification benefits than positive correlations).

The capital asset pricing model (CAPM) asserts that investors will hold only fully diversified portfolios. Hence, total risk as measured by the standard deviation is not relevant because it includes specific risk (which can be diversified away).

Under the CAPM, beta measures the systematic risk of an individual security or portfolio. Beta is the slope of the characteristic line that relates a security's returns to the returns of the market portfolio. By definition, the market itself has a beta of 1.0. The beta of a portfolio is the weighted average of the betas of each security contained in the portfolio. Portfolios with betas greater than 1.0 have systematic risk higher than that of the market; portfolios with betas less than 1.0 have lower systematic risk. By adding securities with betas that are higher (lower), the systematic risk (beta) of the portfolio can be increased (decreased) as desired.

15(b). Without performing the calculations, one can see that the portfolio return would increase because: (1) Real estate has an expected return equal to that of stocks. (2) Its expected return is higher than the return on bonds.

The addition of real estate would result in a reduction of risk because: (1) The standard deviation of real estate is less than that of both stocks and bonds. (2) The covariance of real estate with both stocks and bonds is negative.

The addition of an asset class that is not perfectly correlated with existing assets will reduce variance. The fact that real estate has a negative covariance with the existing asset classes will reduce risk even more.

15(c). Capital market theory holds that efficient markets prevent mispricing of assets and that expected return is proportionate to the level of risk taken. In this instance, real estate is expected to provide the same return as stocks and a higher return than bonds. Yet, it is expected to provide this return at a lower level of risk than both bonds and stocks. If these expectations were realistic, investors would sell the other asset classes and buy real estate, pushing down its return until it was proportionate to the level of risk.

Appraised values differ from transaction prices, reducing the accuracy of return and volatility measures for real estate. Capital market theory was developed and applied to the stock market, which is a very liquid market with relatively small transaction costs. In contrast to the stock market, real estate markets are very thin and lack liquidity.

4.CFA Examination I (1990)

199920034(a). Operating Margin = (Operating Income Depreciation)/Sales

= (38 - 3)/542 = 6.46% = (76-9)/979 = 6.84%

Asset Turnover = Sales/Total Assets

= 542/245 = 2.21x = 979/291 = 3.36x

Interest Burden = Interest Expense/Total Assets

= 3/245 = 1.22% = 0/291 = 0%

Financial Leverage = Total Assets/Common Shareholders Equity

= 245/159 = 1.54x = 291/220 = 1.32x

Tax Rate = Income Taxes/Pre-tax Income

= 13/32 = 40.63% = 37/67 = 55.22%

The recommended formula is:

Return on (ROE) = [(Op. Margin x Asset Turnover) - Int. Burden] x Equity Financial Leverage x (100% - Income Tax Rate)

1999= [(6.46% x 2.21x) - 1.22%] x 1.54 x (100%- 40.63%)

=13.05x 1.54x.5937=11.93%

2003= [(6.84% x 3.36x) - 0%] x 1.32 x (100% - 55.22%)

= 22.98 x 1.32 x .4478 = 13.58% Two alternative approaches are also correct.

ROE = [(Op. Margin - (Int. Burden/Asset Turnover)] x Financial Leverage x Asset Turnover x (100% - Income Tax Rate)

ROE = [(Financial Leverage x Asset Turnover x Operating Margin) - (Financial Leverage x Interest Burden)] x (100% - Income Tax Rate)

4(b). Asset turnover measures the ability of a company to minimize the level of assets (current and fixed) to support its level of sales. The asset turnover increased substantially over the period thus contributing to an increase in the ROE.

Financial leverage measures the amount of financing outside of equity including short and long-term debt. Financial leverage declined over the period thus adversely affected the ROE. Since asset turnover rose substantially more than financial leverage declined, the net effect was an increase in ROE.

3.CFA Examination I (1985)

3(a). Overall, both managers added value by mitigating the currency effects present in the Index. Both exhibited an ability to "pick stocks" in the markets they chose to be in

(Manager B in p articular). Manager B used his opportunities not to be in stocks quite effectively (via the cash/bond contribution t o return), but n either o f t hem m atched the passive index in picking the country markets in which to be invested (Manger B, in particular).

MANAGER AMANAGER BSTRENGTHSCurrency ManagementCurrency Management Stock Selection

Use of Cash/Bond Flexibility

WEAKNESSESCountry SelectionCountry Selection

(to a limited degree)3b. The column reveals the effect on performance in local currency terms after adjustment for movements in the U.S. dollar and, therefore, the effect on the portfolio. Currency gains/losses arise from translating changes in currency exchange rates versus the U.S. dollar over the measuring period (3 years in this case) into U.S. dollars for the U.S. pension p tan. The Index mix 1 ost 12.9% to the dollar, reducing what would otherwise have been a very favorable return from the various country markets of 19.9% to a net return of only 7.0%.

11. CFA Examination I (1992)

11(a). The formula for the constant growth discounted dividend model is shown below:

Do (1 + g)

Price =

where Do = current dividend per share k-g1.20(1 + .08)

For Eastover: Price = =1.296/.03 = $43.200.11- 0.08

This compares with its current stock price of 28. On this basis, it appears that Eastover is undervalued.

11(b). The formula for the two-stage discounted dividend model is as follow:

D1Price=_ l+k

For Eastover:D2D3P3+++

(1+k)2 (1+k)3(1+k) 3

g1= .12,g2 = .08

Do1.20

D11.20*1.121.34

D21.20*(1.12)21.50

D31.20*(1.12)31.69

D4D3*(1.08)1.82

P31.82 411- .08)60.67

1.34 1.501.6960.67

Price = + + +

1.11 (1.11)2 (1.11)3 (1.11)3= 1.2072 + 1.2174 + 1.2357 + 44.3614 = $48.03

This approach indicates that Eastover is even more undervalued than was the case with the constant growth approach.

An alternative solution to the two-stage model is:

D1D2Price =+P2+

(l+k)2

_

l+k(1+k)2

Do1.20

D11.20*1.12=1.34

D21.20*(1.12)2=1.50

D31.20*(1.12)3 =1.69

P21.69/(.11-.08)=56.33

Price =1.34 +1.50+

56.33

1.11 (1.11)2

(1.11)2= 1.21 + 1.22 + 45.72 = $48.15This answer differs from previous answer because of round off error. 11(c). Constant growth model:

Advantages:1) logical, theoretical basis

2) simple to compute

3) inputs can be estimated

Disadvantages:1) very sensitive to inputs of growth

2) g and k difficult to estimate accurately

3) result is meaningless if g > k

4) constant growth is an unrealistic assumption

5) assumes growth will never slow down

6) dividend payout must remain constant

7) not usable for firm not paying dividend

8) assumes stock price will increase at g

Improvements with the two-stage model:1. The two-stage model is more realistic. It accounts for low, high, or zero growth in

the first stage, followed by constant long-term growth in the second stage.

2. The model can solve for stock value when the growth rate in the first stage exceeds

the required rate of return.

13.CFA Examination I (1993)

13(a). The formula for a multistage DDM model with two distinct growth stages consisting of a first stage with five years of above-normal constant growth followed by a second stage of normal constant growth is:

P= D1 + D2 + D3_ + D4_ + D5_ + D6/126/(r- g)(1 + r)' (1 + r)2 (1 + r)3 (1 + r)4 (1 + r)5(1 + r)5p= $2.29 + $2.75 + $3.30 + $3.96 + $4.75 + $5.08/(0.10 - 0.07) (1.10)' (1.10)2 (1.10)3 (1.10)4 (1.10)5 (1.10)5Po= $117.62Note: Though referred to as a multistage DDM, the use of the so-called "H-Model" is incorrect in this application. The H-Model assumes that the growth rate declines in a linear fashion from the above-normal growth rate of 20% to the normal growth rate of 7%. The problem, as stated, depicts a situation in which the growth rate drops abruptly from 20% to 7% after five years.

13(b).Philip Morris P/E (12/31/91) =$80.25 / $4.24=18.9x

S&P500 P/E (12/31/91)=$417.09 / $16.29=25.6x

Philip Morris relative P/E=18.9x / 25.6x=0.74x

13(c). Philip Morris book value (12/31/91)=$12,512 / 920=$13.60

Philip Morris P/B (12/31/95) =$80.25 / $13.60=5.90x

S&P500 P/B (12/31/95)=$417.09 / $161.08=2.59x

Philip Morris relative P/B=5.90x / 2.59x=2.28x

5.CFA Examination III (1995)

Reasons NewSoft shares may not be overvalued compared with shares of Capital Corporation, despite NewSoft's higher ratios of price to earnings (P/E) and ratios of price to book (P/B) include:

Higher P/E

1 . Prices reflect expected future earnings. If NewSoft's earnings are growing faster than Capital Corp.'s, a higher P/E would be justified.

2. Different accounting practices. Accounting practices affect P/Es based on accounting profits because companies often have different accounting practices (e.g., LIFO/FIFO, depreciation policy, and expense recognition). Historical accounting decisions (e.g., writeoffs) may also affect P/Es. Adjustments for such differences may be required before relative valuations can be properly assessed.

3. Cyclical behavior. Given the cyclical nature of the capital goods sector, the P/E ratio for Capital Corp. may have declined below its five-year average only because recent earnings have risen to a level that analysis indicates is unsustainable.

4. Difference between accounting and economic profits. Accounting profits used to calculate P/Es can differ from economic profits and may or may not be sustainable. NewSoft's earnings performance may be understated (e.g., by expensing noncash items such as goodwill). Capital Corp.'s earnings performance may be overstated (e.g., by using low-cost tiers of LIFO inventory).

5. Differences in industries. Different industries have different valuation levels given by the market. NewSoft is a technology company, but Capital Corp. is a capital goods company.

6. Young versus mature industries. Industries at different points in their life cycles will have different valuations. Young industries often have higher valuations.

Higher P/B

1 . Off-balance-sheet assets. NewSoft may have significant off-balance-sheet assets that are reflected in its stock price but not in its book value. P/Bs have little interpretive value in situations in which intellectual property and human capital are key aspects to company success (e.g., the software industry). Physical plant and equipment are typically small, resulting in high PBs.

2. Nature of assets. Although physical plant and equipment presumably are a larger portion of Capital Corp.'s total value, the nature of its assets will also affect the validity of using book value as a measure of economic value. Assets such as goodwill and plant and equipment may vary greatly in their balance sheet cost versus economic value. For example, Capital Corp.'s balance sheet might include significant goodwill, raising the company's book value but not its stock price.

3. Efficient use of assets. The P/B does not show how efficiently either company is using its assets. To the extent that NewSoft is generating a higher margin of profit with its assets, a higher P/B may be justified.

4. Obsolete assets. Some of Capital Corp.'s assets may be functional but obsolete. The company's lower P/B may merely reflect the limited market value of its plant and equipment and the prospective costs of replacement.

7.CFA Examination I (1993)

7(a). Modified duration is Macaulay duration divided by 1 plus the yield to maturity divided by the number of coupons per year:

Where k is the number of coupons per year. If the Macaulay duration is 10 years and the yield to maturity is 8 percent, then modified duration equals 10/(1+ (.08/2)) = 9.62.

7(b). For option-free coupon bonds, modified duration is a better measure of the bond's sensitivity to changes in interest rates. Maturity considers only the final cash flow, while modified duration includes other factors. These factors are the size of coupon payments, the timing of coupon payments, and the level of interest rates (yield-to-maturity).

7(c). Modified duration increases as the coupon decreases. Modified duration decreases as maturity decreases.

7(d). Convexity measures the rate of change in modified duration as yields change. Convexity refers to the shape of the price-yield relationship and can be used to refine the modified duration approximation of the sensitivity of prices to interest rate changes. Convexity shows the extent to which bond prices rise at a greater rate (as yields fall) than they fall (as yields rise). The effect of duration on price and the effect of convexity on price should be added together to obtain an improved approximation of the change in price for a given change in yield.

10.CFA Examination II (1992)

10(a). If yield-to-maturity (YTM) on Bond B falls 75 basis points: -75 basis points = -75/100 = -.75A in YTM

Pro.Price A = (-modified duration) (A inYTM)+ (1/2)(convexity)(A in YTM)2 = (-6.8)(-.75) + (1/2)(6)(75)2= 5.1+.16875

= 5.27

So the projected price will rise to $105.27 from its current $100 price.

10(b). For Bond A, the callable bond, neither maturity nor cash flow is certain. The analysis of callable bonds can take one of four approaches. The first is to ignore the call feature and analyze on a "to maturity basis." All calculations for yield, duration, and convexity are distorted. Durations are too long and yields are too high.

A second approach is to treat the premium bond selling above the call price on a "to call" basis. The duration is unrealistically short and yields too low.

The most effective approach is to use an option evaluation approach. The callable bond can be decomposed into two separate securities - a non-call bond and an option.

Price of callable Bond = Price of non-callable Bond - Price of Option

Since the option will always have some positive value, the callable bond will always have a price that is less than the non-callable security.

An alternative, but less rigorous approach, is to use horizon analysis. The horizon approach considers the three sources of potential dollar return in analyzing a callable bond. The investor is required to estimate an investment holding period, a reinvestment rate, and a call date.

6. CFA Examination III (1987)

6(a). The manager wishes to be protected from any decline in the government bonds' price (any rise in rates) while maintaining a participation in a price advance, should it occur. The manager also wishes to hold the existing bond position over the next six months. The option strategy best suited for this goal is a protected put strategy.

The manager should purchase the put options in size sufficient to protect the $1.0 million portfolio. The manager should purchase 10 put contracts. In this strategy, the bond portfolio will be protected against any price decline below 98, (the put strike price - the put premium) yet will participate with any price advance on the bond less 2.00 (the put premium).

6(b). The manager is now willing to sell the existing bonds in order to create a portfolio structure that achieves the goal. Two strategic options structures equivalent to the structure in Part A above can be designed as follows:

Alternative 1 Sell the government 8% bonds

Invest the proceeds in the T-bills and buy the appropriate amount of 8% bond futures

Buy the put options to protect against price declines while participating in price advances.

Buying T-bills and futures is equivalent to holding the bonds. The manager could purchase $1.0 million in T-bills and 10 futures contracts.

The manager would complete the option strategy alternative 1 by buying 10 put options. Alternative 2 Sell the government 8% bonds

Invest the proceeds in the T-bills

Buy the appropriate amount of call options

A T-bill plus call option position is equivalent in structure to a bond plus put option position. The bill plus call options provides protection against bond price declines since the investor can only lose the premium on the call option. Participation in any bond price advance is achieved since the call option premium will increase.

Specifically, the manager could purchase $1.0 million in T-bills and 10 call options.

6(c). Given the put-call parity pricing relationship, the put options and call options appear misvalued versus each other.

If the call is correctly priced at 4.00, the put should be priced at:

put =4.00- bond price + present value of strike

=4.00- 100+ 100/1.03

=4.00- 100+ 97.09

=1.09

If the put is correctly priced at 2.00, the call should be priced at:

call = 2.00 + 100 - 100/1.03 = 2.00 + 100 - 97.09 = 4.91The put is overpriced versus the call. Therefore:

(1) in the put buying strategies the put premium appears very fully priced.

(2) in the future buying- put buying strategy, similar comments hold. Also the future appears overvalued.

(3) in the buy bills/buy calls strategy, the call option price appears attractive.

In addition, the price of the future at 101 appears high; however, a fair price for the future would be:

price future = price bond + (bill income - bond income) price = 100+(-1) = 99

The option strategy involving buying T-bills and the call options is recommended.

13.CFA Examination III (1999)

13(a). The number of futures contracts required is:

N = (value of the portfolio/value of the index futures) x beta of the portfolio= [$15,000,000/(1,000 x 250)] x 0.88

= [$15,000,000/250,000] x 0.88

=60x0.88

= 52.8 contracts

Selling (going short) 52 or 53 contract will hedge $15,000,000 of equity exposure.

13(b). Alternative methods that replicate the futures strategy in part A include:

1. Shorting SPDRs. SPDRs would be more expensive than futures to trade in terms of liquidity and transactions costs. Tracking error, in theory, would be higher for futures than for SPDRs, because S&P 500 futures can close under and over fair value. SPDRs do not incur the cost of rolling over, which a position in futures would incur if held longer than one expiration date.

2. Creating a synthetic short futures position using a combination of calls and puts. Either options on the underlying index or options on the futures could be used. Selling an index call option and purchasing an index put option with the same contract specifications would create a synthetic short futures position. This strategy would likely be more costly than futures because two transactions are required. Longer-term options tend to be less liquid than futures and SPDRs. Unlike futures, the option combination can be traded either as a spread or separately. If the call and put are traded separately, bid/ask spreads and market impact may increase the cost of the strategy. Options on some index futures are American style, which may result in the call option being exercised at an inopportune time.

3. Creating a fixed equity swap in which Andrew pays the appreciation and dividends on the portfolio and receives a fixed rate. The price of this transaction is negotiated between the two parties, but in general, the swap would be more costly than the futures hedge. Also, equity swaps are not liquid and may prove difficult to reverse once entered. Unlike futures, which are standardized contracts with no customization possible, this alternative has the advantage of customization; negotiable terms include the length of contract, margin requirements, cost of closing position early, and timing of payments.

4. Shorting a forward contract on the S&P 500 index. The price of this transaction is negotiated between the two parties. Forwards are not liquid, may prove difficult to reverse once entered, and may involve counterparty risk. Unlike futures, which are standardized contracts with no customization possible, this alternative has the advantage of customization; negotiable terms include length of contract, margin requirements, cost of closing the position early, and timing of payments.

10.CFA Examination III (1999)

The Muellers' portfolio can be evaluated in terms of the following criteria:

Preference for "Minimal Volatility." The volatility of the Muellers' portfolio is likely to be much greater than minimal. The asset allocation of 95 percent stocks and 5 percent bonds indicates that substantial fluctuations in asset value will likely occur over time. The asset allocation's volatility is exacerbated by the fact that the beta coefficient of 90 percent of the portfolio (i.e., the four growth stock allocations) is substantially greater than 1.0. Thus the allocation to stocks should be reduced, as should the proportion of growth stocks or higher beta issues. Furthermore, the 5 percent allocation to bonds is in a long-term zero coupon bond fund that will be

highly volatile in response to long-term interest rate changes; this bond allocation should be exchanged for one with lower volatility (perhaps shorter maturity, higher grade issues.)

ii. Equity Diversification. The most obvious equity diversification issue is the concentration of 35% of the portfolio in the high beta small cap stock of Andrea's company, a company with a highly uncertain future. A substantial portion of the stock can and should be sold, which can be done free or largely free of tax liability because of the available tax loss carry forward. Another issue is the 90 percent concentration in high beta growth stocks, which contradicts the Muellers' preference for minimal volatility investments. The same is true of the portfolio's 45 percent allocation to higher volatility small cap stocks. Finally, the entire portfolio is concentrated in the domestic market. Diversification away from Andrea's company's stock, into more value stocks, into more large cap stocks, and into at least some international stocks is warranted.

iii. Asset Allocation (including cash flow needs). The portfolio has a large equity weighting that appears to be much too aggressive given the Muellers' financial situation and objectives. Their below average risk tolerance and limited growth objectives indicate that a more conservative, balanced allocation is more appropriate. The Muellers are not invested in any asset class other than stocks and the small bond fund holding. A reduction in equity investments, especially growth and small cap equities, and an increase in debt investments is warranted to produce more consistent and desired results over a complete market cycle.

In addition, the Muellers have no cash reserve or holdings of short-term high grade debt assets. In the very near future, the Muellers will need $50,000 (up front payment) and at least $40,000 (first year tuition and living expenses) for their daughter's college education, as well as a reserve against normal expenses. In addition, they expect to have negative cash flow each year their daughter is in college, which should lead them to increase their cash reserve. The current portfolio is likely to produce a low level of income because of the large weighting in growth stocks and because the only bond holding is a long-term zero coupon bond fund. Also, the marketability of Andrea's company stock unknown and could present a liquidity problem if it needs to be sold quickly. After their immediate cash needs are met, the Muellers will need a modest, ongoing allocation to cash equivalents.

3.CFA Examination I (1994)

3(a). The Treynor measure (T) relates the rate of return earned above the risk-free rate to the portfolio beta during the period under consideration. Therefore, the Treynor measure shows the risk premium (excess return) earned per unit of systematic risk:

Ti = R;- Rf / Beta where: R; = average rate of return for portfolio i during the specified period

Rf = average rate of return- on a risk-free investment during the specified period a; = beta of portfolio i during the specified period.

Treynor MeasurePerformance Relative to the Market (S&P 500)T =10%-6% / 0 .60 = 6.7%Outperformed Market (S&P 500)TM =12%-6% / 1.00= 6.0%

The Treynor measure examines portfolio performance in relation to the security market line (SML). Because the portfolio would plot above the SML, it outperformed the S&P 500 Index. Because T was greater than TM, 6.7 percent versus 6.0 percent, respectively, the portfolio clearly outperformed the market index.

The Sharpe measure (S) relates the rate of return earned above the risk free rate to the total risk of a portfolio by including the standard deviation of returns. Therefore, the Sharpe measure indicates the risk premium (excess return) per unit of total risk:

S = R; - Rf / 6jwhere: R; = average rate of return for portfolio i during the specified period

Rf = average rate of return on a risk-free investment during the specified period

ai = standard deviation of the rate of return for portfolio i during the specified

period.

Sharpe MeasurePerformance Relative to the Market (S&P 500)S =10% - 6% / 18%

= 0.222% Underperformed Market (S&P 500)SM=12%-6% / 13%

= 0.462%

The Sharpe measure uses total risk to compare portfolios with the capital market line (CML). The portfolio would plot below the CML, indicating that it underperformed the market. Because S was less than SM, 0.222 versus 0.462, respectively, the portfolio underperformed the market.

3(b). The Treynor measure assumes that the appropriate risk measure for a portfolio is its systematic risk, or beta. Hence, the Treynor measure implicitly assumes that the portfolio being measured is fully diversified. The Sharpe measure is similar to the Treynor measure except that the excess return on a portfolio is divided by the standard deviation of the portfolio.

For p erfectly diversified p ortfolios ( that i s, t hose without any unsystematic o r specific risk), the Treynor and Sharpe measures would give consistent results relative to the market index because the total variance of the portfolio would be the same as its systematic variance (beta). A poorly diversified portfolio could show better performance relative to the market if the Treynor measure is used but lower performance relative to the market if the Sharpe measure is used. Any difference between the two measures relative to the markets would come directly from a difference in diversification.

In particular, Portfolio X outperformed the market if measured by the Treynor measure but did not perform as well as the market using the Sharpe measure. The reason is that Portfolio X has a large amount of unsystematic risk. Such risk is not a factor in determining the value of the Treynor measure for the portfolio, because the Treynor measure considers only systematic risk. The S harpe measure, however, c onsiders total risk (that is, both systematic and unsystematic risk). Portfolio X, which has a low amount of systematic risk, could have a high amount of total risk, because of its lack of diversification. Hence, Portfolio X would have a high Treynor measure (because of low systematic risk) and a low Sharpe measure (because of high total risk).

End of Chapter Problems

Chapter:

Problem:

5

4

8

11

11

15

13

4, 6

4.Profit on a Short Sale = Begin.Value - Ending Value - Dividends -Trans. Costs - Interest

Beginning Value of Investment = $56.00 x 100 shares = $5,600 (sold under a short sale arrangement)

Your investment = margin requirement + commission = (.45 x $5,600) + $155

= $2,520 + $155

= $2,675

Ending Value of Investment = $45.00 x 100 = $4,500 (Cost of closing out position)

Dividends = $2.50 x 100 shares = $250.00 Transaction Costs = $155 + $145 = $300.00 Interest = .08 x (.55 x $5,600) _ $246.40 Therefore:

Profit = $5,600 - $4,500 - $250 - $300 - $246.40 = $303.60

The rate of return on your investment of $2,675 is: $303.60/$2,675 = 11.35%

11(a).

For Intel:

COV i,m = (.72)(1210)(0550) = .00479 Beta =.00479 = .00479 =1.597

(.055)2.0030

For Ford:

COV i,m = (.33)(1460)(0550) = .00265

Beta = .00265 / .0030 =.883

For Anheuser Busch:

COV i,m = (.55)(.0760)(0550) = .00230 Beta = 00230 = .767

.0030

For Merck:

COV i,m = (.60)(.1020)(.0550) = .00337 Beta = 00337 =1.123

.0030

1.0

Beta 15(a). Projected Dividends for the next 3 years:

Year 1 ($1.25 x 1.08) =$1.35

Year 2 ($1.35 x 1.08) _$1.46

Year 3 ($1.46 x 1.08) _$1.58

Required rate of return 12% Growth rate of dividends 8%

The present value of the stock is:

V= 1.35/1.12 + 1.46/(1.12)2 + 1.58/(1.12)3 + 40/(1.12) 3 V=1.21+1.16+1.12+28.47 = $31.96

15(b). Growth rate8% 15(c). Required rate of return 12%

V 1.35 = 1.35 /.04 = 33.75.12-.08

15(d). Assuming all the above assumptions remain the same, the price at end of year 3 will be:

PD4/ k g = (1.25 x (1.08)4) / .12-.08 = $42.52

4. (a) Growth = .60 x .12 = .072 = 7.2%

4 (b) P/E .40 / .1-.072 = 14.29x

4(c). The market price will rise to: Price = 14.29 x $53 = $757.37

757.14-950+30

4(d). Rate of Return = 950= -17.14%

6(a). Growth Rates:Required return:

High= (1 - 0.45) x 0.16 = .088High= 0.08 + 0.03 = 0.11

Low= (1 - 0.65) x 0.10 = .035Low= 0.10 + 0.05 = 0.15

Consensus = (1 - 0.55) x 0.13 = .0585Consensus = 0.09 + 0.04 = 0.13

P/E Ratios:

High= 0.45/(0.11 0.088) = 0.45/.022 = 20.4545

Low= 0.65/(0.15 0.035) = 0.65/.115 = 5.6522 Consensus = 0.55/(0.13 0.0585) = 0.55/.0715 = 7.6923Price:

High= 52.87 x 20.4545 = $ 1081.43

Low= 49.40 x 5.6522 = $ 279.22 Consensus = 51.14 x 7.6923 = $ 393.38

6(b). High= (1081.43/1600) -1 = -.3241

Low= (279.22/1600) -1 = -.8255

Consensus= (393.38/1600) -1 = -.7541

Given that large losses are expected, one should underweight the U.S. stocks in a global portfolio.

1 i

L

17-7

E(R) = .08 + .07B1

= .08 + B1(.15- .08)=.08+.07B1StockBetaIntel1.597Ford.883Anheuser Busch.767Merck1.123

11(b). E(R;) = RFR + B;(RM - RFR)

11(c). .20 RM= .15

.10 RFR=.08

.08 + .1118= .1918.08 + .0618= .1418.08 + .0537= .1337.08 + .0786= .1586