FIN 310 - Midterm 2020 - Solutions

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FIN 310 Midterm 2020 – Solutions Question 8 The following assets are available. Asset Expected Return Standard Deviation Classen Blvd (CL) 12% 17% Western Ave. Manufacturing (WAM) 9% 13% 22th Street Industries (IND) 8% 12% T-bills 4% 0% Assume your risk-aversion coefficient is A=2.5. If you had to choose ONE of the above assets, which Would it be? A. I do not know B. It depends C. Classen Blvd D. Western Ave. Manufacturing E. 22th Street industries F. T-bills Question 8 The following assets are available. Asset Expected Return Standard Deviation Classen Blvd (CL) 12% 17% Western Ave. Manufacturing (WAM) 9% 13% 22th Street Industries (IND) 8% 12% T-bills 4% 0% Assume your risk-aversion coefficient is A=2.5. If you had to choose ONE of the above assets, which

Would it be? A. I do not know B. It depends C. Classen Blvd D. Western Ave. Manufacturing E. 22th Street industries F. T-bills Question 1 Below are weekly prices for Lumber Liquidators (LL). Date Feb 16 Feb 8 Feb 1 Jan 25 Jan 19 Jan 15 Prices 14.21 12.33 12.34 12.91 12.30 12.15 If you sold 2000 shares of Lumber Liquidators short at the end of trading on January 15, what would your return be on by the end of trading on February 16? The initial margin is 50%. A.+34% B.-34% C.-17% D.+17% E. Not enough information Correct Answer - B You sell Lumber Liquidators short for $12.15 on January 15 and buy back the shares for $14.21 on February 16. Your initial margin is 50% so you put up $6.075 (0.5*12.15) of your own money. Note that calculating the return for one share gives you the same answer as calculating the return for 100 shares. Your return is, HPR = 12.15 − 14.21 6.075 =− 0.339 ∨− 33.9% Question 2 Below are weekly prices for Lumber Liquidators (LL). Date Feb 16 Feb 8 Feb 1 Jan 25 Jan 19 Jan 15 Prices 14.21 12.33 12.34 12.91 12.30 12.15 You sold 2000 shares of Lumber Liquidators short at the end of trading of January 15. Your initial margin is 50%. If the maintenance margin is 35%, you get a margin call on:

I. Feb 16 II. Feb 8 III. Feb 1 IV. Jan 25 V. Jan 19 VI. Jan 15 A. I B.I and IV C.I, II, III, IV, V D.VI E.II, III, IV and V F. You never get a margin call Correct Answer – A This problem can be done two ways. The easiest is to calculate the price at which you get a margin call. You get a margin call when the margin reaches the maintenance margin of 35%. Your equity is the money you put up from your own pocket (6.075*100=607.5) plus the sales proceeds (1215), 0.35 = Margin = Equity Value of Securities = 1822.5 − 100 P 100 P Solve for the price (P), P = 13.50 You get a margin call on February 16 as the price is above 13.5 The other way to solve this problem is to calculate the margin for each date - this is not the quickest way to solve the problem. For instance, do you get a margin call on January 25 when the price is 12.91? Margin = 1822.5 − 100 ∗ 12.91 100 ∗ 12.91 = 41.17% No, you do not get a margin call on January 25 as the margin is above the maintenance margin of 35%. Then check February 16, Margin = 1822.5 − 100 ∗ 14.21 100 ∗ 14.21 = 28.25% Yes, you do get a margin call on February 16 as the margin is below the maintenance margin of 35%.

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Question 3 Below are weekly prices for Lumber Liquidators (LL). Date Feb 16 Feb 8 Feb 1 Jan 25 Jan 19 Jan 15 Prices 14.21 12.33 12.34 12.91 12.30 12.15 You buy 4000 shares of Lumber Liquidators on margin on January 15. In violation of the federal minimum, your initial margin is 25%. If the maintenance margin is 20%, you get a margin call on: I. Feb 16 II. Feb 8 III. Feb 1 IV. Jan 25 V. Jan 19 VI. Jan 15 A. You never get a margin call B.I C.I and IV D.II, III, V E.VI F.IV Correct Answer – A The easiest way to solve these types of problems is typically to calculate the price at which you get a margin call – the alternate (but not the most efficient) way to solve this is presented in Question 2 above. You get a margin call when the margin reaches the maintenance margin of 20%. This calculation is per share (in Question 2 I presented how to solve this problem by using your total position – looking at only one share is often quicker). Your liabilities are 12.15*0.75=9.12 , 0.2 = Margin = Equity Value of Securities = P − 9.12 P = 11.4 You never get a margin call as the price never falls to 11.4 You can in fact solve this problem without the calculation. When you buy on margin you only

get a margin call if the price falls below the initial price (here: 12.15). As the price never goes below 12.15 you never get a margin call. Question 4 Below are weekly prices for Lumber Liquidators (LL). Date Feb 16 Feb 8 Feb 1 Jan 25 Jan 19 Jan 15 Prices 14.21 12.33 12.34 12.91 12.30 12.15 If you could purchase a stock tip that told you with 100% certainty that LL would rise in price from 12.15 to 14.21 from Jan 15 to Feb 16, how much would you pay for this tip? Assume you have $4000 in your bank account on January 15 and that the initial margin requirement is 50%. The annual interest rate on margin loans is 0%. You can only trade once during this period. A.1356 B. up to 1000 C.680 D. An infinite amount E. I would not pay for the stock tip Correct Answer – A The HPR is, HPR = 14.21 − 12.15 12.15 ( 0.5 ) = 34% Note that this is the opposite (positive instead of negative) of Question 1 – there we shorted the asset whereas here we buy on margin. Therefore, you can make the following from the stock tip, 4000 ( 0.34 ) = 1356 The most you would pay for the stock tip is 1356 – at that price you break even. The correct answer is that you would pay up to 1356 for the stock tip. Note that as the solution say ‘1356’ (and not ‘up to 1356’) there is some ambiguity here. Solution B (up to 1000) is clearly incorrect as you’d be willing to pay above 1000 too. D is clearly incorrect as the max you could make is 1356. E is also wrong as the stock tip is valuable.

However, you could make a case for paying 680 for the stock tip – and case that 680 is better than 1356 (as you make more money). Therefore, full credit is awarded for both C and A. Question 5 Below are weekly prices for Lumber Liquidators (LL). Date Feb 16 Feb 8 Feb 1 Jan 25 Jan 19 Jan 15 Prices 14.21 12.33 12.34 12.91 12.30 12.15 What is your best guess of what LL's weekly expected return will be after Feb 16? A. 3.3% B. -3% C. $12.7 D. 3.9% E. 15% Correct Answer - A Your best guess – given this limited historical information you have – is the sample mean. First calculate the HPRs. For example, from Jan 15 to Jan 19, HPR = 12.30 − 12.15 12.15 = 0.012 ∨ 1.2% Similarly all the HPRs are 1.2%, 5.0%, -4.4%, -0.00%, 15% m = 1.2% + 5% − 4.4% + 0% + 15% 5 = 3.4% You can get slightly different answers depending on rounding and depending on if you count the first period (between Jan 15 and Jan 19) as a whole week or not, but regardless the best answer (i.e., closest answer) will be A. Question 6 Below are weekly prices for Lumber Liquidators (LL). Date Feb 16 Feb 8 Feb 1 Jan 25 Jan 19 Jan 15

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Prices 14.21 12.33 12.34 12.91 12.30 12.15 How volatile is the return on LL stock? A. $0.78 B. 7.4% C. 6.7% D. 6.6% E. 0.44% Correct Answer - B Your best guess of the true volatility (i.e., the true standard deviation) is the sample standard deviation of weekly HPRs. Using the weekly HPRs from Question 5 you can calculate this in Excel using STDEV.S (as on Project 1). Alternatively you can calculate this manually – but that is slower. s 2 = ( 1.2 − 3.4 ) 2 + ( 5 − 3.4 ) 2 + ( − 4.4 − 3.4 ) 2 + ( 0 − 3.4 ) 2 + ( 15 − 3.4 ) 2 4 s = 7.4% Question 7 The following assets are available. Asset Expected Return Standard Deviation Classen Blvd (CL) 12% 17% Western Ave. Manufacturing (WAM) 9% 13% 22th Street Industries (IND) 8% 12% T-bills 4% 0% If you are somewhat risk-averse which asset do your prefer? A. I do not know B. Classen Blvd C. Western Ave. Manufacturing D. 22th Street Industries E. T-Bills F. An equally weighted portfolio of all four assets

Correct Answer – A As no asset in dominant (i.e., dominates all others) we cannot say which one we prefer unless we know how risk averse we are (i.e., we need to know your coefficient of risk aversion (A)). Question 8 The following assets are available. Asset Expected Return Standard Deviation Classen Blvd (CL) 12% 17% Western Ave. Manufacturing (WAM) 9% 13% 22th Street Industries (IND) 8% 12% T-bills 4% 0% Assume your risk-aversion coefficient is A=2.5. If you had to choose ONE of the above assets, which Would it be? A. I do not know B. It depends C. Classen Blvd D. Western Ave. Manufacturing E. 22th Street industries F. T-bills Correct Answer – C Calculate how much utility you get from each asset. U CL = E ( r CL ) − 0.5 Aσ CL 2 = 0.12 − 0.5 ( 3 ) ( 0.17 ) 2 = 0.0767 U WAM = 0.09 − 0.5 ( 3 ) ( 0.13 ) 2 = 0.0647 U IND = 0.08 − 0.5 ( 3 ) ( 0.12 ) 2 = 0.0584 U r f = 0.04 − 0.5 ( 3 ) ( 0 ) 2 = 0.04 As Classen Blvd. Inc. (CL) gives you the highest utility, select CL. Question 9 The following assets are available.

Asset Expected Return Standard Deviation Classen Blvd (CL) 12% 17% Western Ave. Manufacturing (WAM) 9% 13% 22 nd Street Industries (IND) 8% 12% T-bills 4% 0% Assume the CAPM assumptions hold. Describe the optimal risky portfolio. Include the optimal portfolio weights. Explain. The optimal risky portfolio is the portfolio with the best risk-return tradeoff (i.e., the highest Sharpe Ratio) – and it contains all publically traded risky securities. If there are only three assets available then the optimal risky portfolio contains CL, WAM and IND. The optimal portfolio weights according to the CAPM are proportional to the market value of the security – to be exact: the market value of the security divided by the market value of all securities. Therefore, the portfolio weights are: w CL = M V CL M V CL + M V WAM + M V IND Question 10 The following assets are available. Asset Expected Return Standard Deviation Classen Blvd (CL) 12% 17% Western Ave. Manufacturing (WAM) 9% 13% 22 nd Street Industries (IND) 8% 12% T-bills 4% 0% Mr. Invest-A-Lot is risk averse. If you want to find the portfolio that gives Mr. Invest-A-Lot the highest utility, what information would you need beyond what is available above? Explain. To find the best portfolio (i.e., the one that maximizes utility) you first have to know the optimal risky portfolio. To find this portfolio you would need – in addition to the expected returns and standard deviations above – the covariance between all the securities. Then you can find the optimal portfolio which is the one that maximizes the Sharpe Ratio (i.e., has the best risk-return tradeoff).

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Lastly, to find how much you should invest in the optimal risky portfolio ¿ and how much you should invest in the risk-free portfolio ¿ you need to know your risk aversion coefficient A. Question 11 Under the CAPM we assume that all investors… I. are the same II. have identical holding periods III. apply the techniques in portfolio theory to find their optimal portfolio IV. estimate the same expected returns for Apple, Facebook and Microsoft V. hold the same optimal risky portfolio VI. have the same level of risk aversion Correct Answer - C The CAPM assume all investors are the same except for risk aversion – this includes having the same expectations for future expected returns (therefore IV is a CAPM assumption). Therefore I and VI are not CAPM assumptions. Moreover, V is not a CAPM assumption, but an implication (i.e., consequence) of the CAPM assumptions. Question 12 Below are weekly prices for Lumber Liquidators (LL). Date Feb 16 Feb 8 Feb 1 Jan 25 Jan 19 Jan 15 Prices 14.21 12.33 12.34 12.91 12.30 12.15 You can purchase a stock tip that tells you with 100% certainty what LL stock price will do from Jan 15 to Feb 16. Assume you can trade once a week from Jan 15 to February 16. What is your optimal trading strategy? No calculations are necessary for full credit. Explain why your strategy is optimal. The minimal margin is 50%. You know what will happen so you always use a minimum margin of 50% to maximize your gains. Your trading strategy is: 1. Buy LL on margin on Jan 15. Sell on Jan 25. 2. Sell LL short on Jan 25. Buy back the shares on Feb 8 to close out the short sale. 3. Buy LL on margin on Feb 8. Sell on Feb 16.

Question 13 The following assets are available, Asset Expected Return Standard Deviation Beta Stock A 12.5% 16% 1.5 Portfolio XYZ 23% 50% 3 Market Portfolio 9% 14% 1 T-bills 2% 0% 0 Your risk aversion coefficient is A = 5 . What is the optimal portfolio for a CAPM investor? Correct Answer - F The CAPM investor invests in the market portfolio (i.e., the optimal risky portfolio) and the risk- free asset. y ¿ = E ( r m ) − r f σ m 2 A = 0.09 − 0.02 0.14 2 ( 5 ) = 0.71 Therefore, a CAPM investor with a risk aversion coefficient of 5 invests 71% in the market portfolio and 29% in T-bills (i.e., the risk-free asset). Question 14 The following assets are available, Asset Expected Return Standard Deviation Beta Stock A 12% 16% 1.5 Portfolio XYZ 15% 30% 3 Market Portfolio 9% 14% 1 T-bills 2% 0 0 Is this consistent with the CAPM? Explain. First, we need to check that all the securities are on the SML (i.e., the CAPM equation holds). E ( r A ) = r f + β A ( E ( r m ) − r f ) = 2% + 1.5 ( 9% − 2% ) = 12.5% E ( r XYZ ) = 2% + 3 ( 9% − 2% ) = 23%

No, the CAPM does not hold. The return on Stock A is too low and the return on Portfolio XYZ is also too low relative to what the CAPM says. You can also check that two securities have lower Sharpe Ratios than the Market Portfolio – in the CAPM the market portfolio always has the best risk-return tradeoff. S R M = 9% − 2% 14% = 0.5 S R A = 12% − 2% 16% = 0.625 S R XYZ = 15% − 2% 30% = 0.433 As Stock A has a Sharpe Ratio that is higher than the Sharpe Ratio of the market, this is inconsistent with the CAPM. Question 15 The article “Apple Added to the Dow” discusses the addition of Apple to the Dow Jones Industrial Average (DJIA) while the article. The article "An Old Dog Barks" discusses how the Dow Jones Industrial Average (DJIA) reached a new high. Referring to the arguments in the articles and the discussion in the video lecture answer the following question: The goal of the DJIA is to track the performance of US stock markets. Does the DJIA achieve this goal? Give at least one argument in favor and one against. Arguments for the DJIA achieving this goal are: (1) The index is constructed with this in mind. The index is changed (and companies added/removed) to try and achieve the goal of the DIJA representing the performance of US stock markets. (2) The correlation between the DIJA and broader indices (e.g., the S&P 500 and Russell 3000) is high – these indices also share the goal of tracking the performance of US stock markets. This means that in practice the DIJA does a decent job of tracking the performance of US stock markets.

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(3) The DJIA is prominently featured in the press as a measure of stock market (and economic performance overall) – which it likely would not be if it did a poor job of tracking US stock markets. Arguments against the DJIA achieving this goal are: (1) The index is price weighted (rather than market value weighted) which can make it less representative. (2) The index only includes 30 companies which make it less likely to be able to track US stock markets than broader indices that include many more stocks. Question 16 In the past, penny stocks were considered any stocks that traded for less than one dollar per share. The U.S. Securities and Exchange Commission (SEC) has modified the definition to include all shares trading below five dollars. The SEC is an independent federal government agency responsible for protecting investors as they maintain fair and orderly functioning of the securities markets. Penny stocks are often growing companies with limited cash and resources. Penny stocks are usually associated with small companies and trade infrequently meaning they have a lack of liquidity or ready buyers in the marketplace. Typically, penny stocks have a higher level of volatility. Make a case for investing in penny stocks. Then make a case against investing in penny stocks. The case for investing in penny stocks: 1. Penny stocks may have higher returns which can justify the higher volatility. 2. Illiquid stocks can have higher returns to compensate for illiquidity risk. 3. If you trading horizon is long you are benefits more from the higher risk premium and are less adversely affect by the low liquidity. The case against investing in penny stocks: 1. Illiquidity can make it difficult (i.e., costly) to buy and sell penny stocks. 2. Any extra return you get may not be justified by the risk (i.e., the Sharpe Ratios are low) 3. Some penny stocks do not provide access to reliable financial information about the firm. Not all of these arguments are required for full credit.

Question 17 You have some surplus cash right now, but you plan to spend it in five years. Make a case for investing in T-bills. Then make a case for investing in stocks. What can you do to help decide between T-bills and stocks? The case for investing in T-bills: Your trading horizon is somewhat short and T-bills returns are less volatile. This increased certainty can compensate for the lower returns on T-bills. The case against investing in T-bills T-bills have significantly lower returns than alternatives such as stocks. You would be missing out on the market risk premium (i.e., if you invest in the market portfolio) for five years. Five years is not a long horizon, but it is not very short either. To decide it would be useful to know your coefficient of risk aversion (A). This would enable you to determine how much you should optimally allocate to T-bills ( 1 − y ¿ ¿ and risky securities ¿ . Question 18 ” Do you really like a particular stock? Put 10% or so of your portfolio on it. Make the idea count. Good investment ideas should not be diversified away into meaningless oblivion “ - Bill Gross Do you agree or disagree with this statement? Explain. You can make a case for either agreeing or disagreeing, but it is easier to make a convincing case for disagreeing here. The case for agreeing: If you have superior information about the future stock price (i.e., information that other investors do not have) then you can achieve a superior Sharpe Ratio by investing in the stock. If you are very confident that this information is accurate then you can make case for investing more than 10% in the stock – and not diversifying. That said ‘liking’ the stock will not get you superior information. You need information about the

future direction of the stock price. The case for disagreeing: It is very difficult to have superior information about future stock returns that other investors do not have. Moreover, diversified portfolios on average tend to have higher Sharpe Ratios as you eliminate unique risk. The optimal portfolio in portfolio theory (and in CAPM) is a well-diversified portfolio containing all publically traded securities. Question 19 Uncle Tom says US stocks always outperform foreign stocks. Therefore you should only invest in US stocks he claims. Do you agree or disagree with your Uncle's investment advice? Why or why not. Disagree. What your uncle is suggesting is essentially in extreme case of home bias i.e., he is recommending investing 100% at home and nothing abroad. You can achieve a higher expected Sharpe Ratio by diversifying into foreign stocks. This is because foreign stocks are less than perfectly correlated with US stocks allowing you to diversify away more risk and obtain a better risk-return tradeoff (i.e., Sharpe Ratio). Question 20 How are the SML, CAL and CML related? How are they different? The CAL is the Capital Allocation Line. It contains all the possible combinations of risk and return you can obtain by investing in a risky and a risk-free asset. There is an upwards sloping relationship between risk and return. The CML is the Capital Market Line. It contains all the possible combinations of risk and return (i.e., portfolios) you can obtain by investing in the market portfolio and the risk-free asset. The CML is a special case of the CAL where the risky portfolio is the market portfolio. In the CAPM all risky assets – except for the market portfolio – plot below the CML. The SML is the Security Market Line. It is a graph of the CAPM equation. The SML shows the relationship between the beta (market risk) and expected returns – the higher a security’s beta the higher the return. If the CAPM assumptions hold then in equilibrium all assets are on the SML.

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Question 21 – FALSE Domestically investors only really look at three stock market indices - the Nasdaq Composite, the S&P 500 and the Dow Jones Industrial Average. There are many other stock market indices investors use (e.g., Wilshire 5000 Russell 2000, Russell 3000 etc.) – the Dow, Nasdaq and S&P 500 are merely the most popular ones. Question 22 – FALSE Given a choice between two assets you should always choose the most liquid one. All else constant you would choose the most liquid one, however, all else may not be constant. For example, illiquid stocks tend to have higher returns (to compensate for liquidity risk). Question 23 – FALSE The CAPM implies that all investors hold the same portfolio. This is incorrect for two reasons. First, an implication of the CAPM is that all investors hold the same optimal RISKY portfolio – this is an implication not an assumption. Second, CAPM investors hold different overall portfolios as CAPM investors have different levels of risk aversion which implies that the amount they optimally allocate to the optimal risky portfolio and the risk asset differs (i.e., they have different y ¿ ). Question 24 – TRUE If the initial margin is the same then short selling and buying on margin about equally risky. Yes, if the initial margin is the same (i.e., the leverage is the same) than both these trading strategies are equally risky (i.e., have similar standard deviations). Question 25 - TRUE In some settings it is possible to accurately calculate the true mean and true variance. Yes. For example, we can do this for games of chance – or in game shows (see the risk tolerance video example on BB). We cannot do this for risky securities; however, the statement was more general than that.

FIN 310 - Midterm 2020 - Solutions

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