fin 406 homework problems
Stocks with a beta of zero offer an expected rate of return of zero.
False. β = 0 implies E(r) = rf , not zero. `
One month ago, a share of Apple stock (AAPL) was worth $192. Today it is worth $216. What is the 1-month return on AAPL?
(216-192)/192 = 12.5%
net asset value formula
(market value of assets - market value of liabilities) / shares outstanding
premium or discount formula
(price - NAV) / NAV
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Your risky portfolio includes the following investments in the given proportions: Stock A 27%, Stock B 33%, Stock C 40% Your client decides to invest in your risky portfolio a proportion (y) of his total investment budget with the remainder in a T-bill money market fund so that his overall portfolio will have an expected rate of return of 15%. a. What is the proportion y? (Round your answer to 1 decimal place.) Proportion y b. What are your client's investment proportions in your three stocks and the T-bill fund? (Round your answers to 1 decimal place.) Security InvestmentProportionsT-Bills%Stock A%Stock B%Stock C% c. What is the standard deviation of the rate of return on your client's portfolio? (Round your answer to 1 decimal place.) Standard deviation % per year
1. Mean = (0.30 7%) + (0.7 17%) = 14% per Year Standard Deviation = 0.70 * 27% = 18.9% per Year 2. Mean Return on Portfolio = Rf + (Rp - Rf)y= 7% + (17% - 7%)y = 7% + 10%y If the mean of the portfolio is equal to 15%, then solving for y we will get 15% = 7% + 10%yy = (15% - 7%) / 10% = 0.83. (a) Mean Return on Portfolio = Rf + (Rp - Rf)y= 7% + (17% - 7%)y = 7% + 10%y Thus in order to obtain a mean return of 15%, the client must invest 80% of total funds in the risky portfolio and 20% in treasure bills. (b). Investment proportions of the client's funds: 20% in T bills, 0.8 *27% = 21.6% in stock A, 0.8 * 33% = 26.4% in stock B, 0.8 * 40% = 32.0% in Stock C c. standard deviation = the square root of .8 squared * .27 squared
During a particular year, the T-bill rate was 6%, the market return was 14%, and a portfolio manager with beta of .5 realized a return of 10%. Evaluate the manager based on the portfolio alpha.
E(r) CAPM = .06 + .5(.14 - .06) = .1 alpha = .10 - .10 = 0
Give an example of three financial intermediaries, and explain how they act as a bridge between small investors and large capital markets or corporations.
1. Mutual funds accept funds from small investors and invest, on behalf of these investors, in the national and international securities markets. 2. Pension funds accept funds and then invest, on behalf of current and future retirees, thereby channeling funds from one sector of the economy to another. 3. Venture capital firms pool the funds of private investors and invest in start-up firms. 4. Banks accept deposits from customers and loan those funds to businesses or use the funds to buy securities of large corporations.
a. Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 1 decimal place.) b. Suppose your risky portfolio includes the following investments in the given proportions: stock A: 27% stock B: 33% stock C: 40% What are the investment proportions of your client's overall portfolio, including the position in T-bills? c. What is the reward-to-volatility ratio (i.e. the Sharpe ratio S) of your risky portfolio and your client's overall portfolio?
1. Portfolio Expected Return: w1E(r1)+w2(E(r2)(.3.07)+(.7.17)=14% per year 2. Standard Deviation.7*.27=18.9% per year T- Bill- 30% (from question) Stock A: .27*.7= 18.9% Stock B: .33*.7= 23.1% Stock C: .40*.7= 28%
You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client's portfolio?
14. in practice
What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 15%?
15%
y = 5x + 3
5 is the slope, 3 is the intercept
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 13% with a standard deviation of 25%. a. What is the slope of the CML?
= (13% - 7%)/25% = 0.24
A portfolio's expected return is 12%, its standard deviation is 20%, and the risk-free rate is 4%. Which of the following would make for the greatest increase in the portfolio's Sharpe ratio? (Select all that apply. For correct answer(s), click the option to place a check mark. For incorrect answer(s), leave blank.) A 1 percentage point increase in expected return.checked A 1 percentage point decrease in the risk-free rate.checked A 1 percentage point decrease in its standard deviation.
A 1 percentage point increase in expected return A 1 percentage point decrease in the risk-free rate
What are some differences between a unit investment trust and a closed-end fund?
A unit investment trust is an unmanaged mutual fund. Its portfolio is fixed and does not change due to asset trades, as does a close-end fund. Investors who wish to liquidate their holdings of a unit investment trust may sell the shares back to the trustee for net asset value, while a close-end fund is traded on the open market.
Choose the correct answer in the following statements about financial and real assets. a. Toyota takes out a bank loan to finance the construction of a new factory. b. Toyota pays off its loan. c. Toyota uses $10 million of cash on hand to purchase additional inventory of spare auto parts.
A.) Toyota creates a real asset—the factory. The loan is a financial asset that is created in the transaction B.) When the loan is repaid, the financial asset is destroyed but the real asset continues to exist. C.) The cash is a financial asset that is traded in exchange for a real asset, inventory.
What is the difference between asset allocation and security selection?
Asset allocation is the allocation of an investment portfolio across broad asset classes. Security selection is the choice of specific securities within each asset class.
Suppose we are given the following info: Expected Return Standard Deviation T-Bills expected return: rf = 4%; standard deviation f = 0 S&P 500 (asset P)E[rP] = 12%; σP = 20% Consider an investor, David, whose risk aversion (Coefficient A) is assumed to be 3.5 Compute his optimal (complete) portfolio, using the formula of the optimal (complete) portfolio given in Eq. (4) in the notes.
E(r) = 12% rf = 4% A = 3.5 risk aversion standard dev = 20% y = (E(r) - rf) / (A * stand dev squared)) y = (.12 - .04) / 3.5 (.20 squared) = .571 optimal portfolio with 57.14% investment in risky asset
What are the advantages and disadvantages of exchange-traded funds versus mutual funds?
Exchange-traded funds can be traded during the day, just as the stocks they represent. They are most tax effective, in that they do not have as many distributions. They have much lower transaction costs. They also do not require load charges, management fees, and minimum investment amounts. The disadvantage is that ETFs must be purchased from brokers for a fee. Moreover, investors may incur a bid-ask spread when purchasing an ETF.
The CAPM implies that investors require a higher return to hold highly volatile securities.
False. Investors require a risk premium only for bearing systematic (undiversifiable or market) risk. Total volatility includes diversifiable risk.
You can construct a portfolio with beta of .75 by investing .75 of the investment budget in T-bills and the remainder in the market portfolio.
False. Your portfolio should be invested 75% in the market portfolio and 25% in T-bills. Then: βP = (0.75 × 1) + (0.25 × 0) = 0.75
What are some differences between hedge funds and mutual funds?
Hedge funds have much less regulation since they are part of private partnerships and free from most SEC regulation. They permit investors to take on many risks unavailable to mutual funds. Hedge funds, however, may require higher fees and provide less transparency to investors. This offers significant counter party risk and hedge fund investors need to be more careful about the firm they invest with.
Why are money market securities sometimes referred to as "cash equivalents"?
Money market securities are referred to as "cash equivalents" because of their great liquidity. The prices of money market securities are very stable, and they can be converted to cash (i.e., sold) on very short notice and with very low transaction costs.
What are the differences between real and financial assets?
Real assets are assets used to produce goods and services. Financial assets are claims onreal assets or the income generated by them.
Why do most professionals consider the Wilshire 5000 a better index of the performance of the broad stock market than the Dow Jones Industrial Average?
While the DJIA has 30 large corporations in the index, it does not represent the overall market nearly as well as the more than 5000 stocks contained in The Wilshire index. The DJIA is simply too small.
A plan sponsor with a portfolio manager who invests in small-capitalization, high-growth stocks should have the plan sponsor's performance measured against which one of the following? S&P 500 Wilshire 5000 DJIA Russell 2000
Russell 2000 index the other 3 are used in the condition when stocks have high cap and low growth
The average rate of return on investments in large stocks has outpaced that on investments in Treasury bills by about 7% since 1926. Why, then, does anyone invest in Treasury bills?
Treasury bills serve a purpose for investors who prefer a low-risk investment. The lower average rate of return compared to stocks is the price investors pay for predictability of investment performance and portfolio value.
the security market line depicts:
a security's expected return as a function of its systematic risk
You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the reward-to-volatility ratio (i.e. the Sharpe ratio) for the equity fund?
expected return of equity = 10% + 6% = 16% standard deviation = 14% reward to voltality ratio = expected return - risk free rate /standard deviation = 16% -6%/14% = 0.71
Investors should expect a higher return from holding portfolio A versus portfolio B under capital asset pricing theory (CAPM). Assume that both port-folios are fully diversified. portfolio A: systematic risk 1, high specific risk for each individual security portfolio B: systematic risk 1, low specific risk for each individual security
false, since both portfolios are fully diversified, it doesn't matter if the specified risk for each individual security is high or low; the specific risk has been diversified away for both portfolios
What do you think would happen to the expected return on stocks if investors perceived an increase in the volatility of stocks? Assuming no change in tastes, that is, an unchanged risk aversion, investors perceiving higher risk will demand a higher risk premium to hold the same portfolio they held before. If we assume that the risk-free rate is unaffected, the increase in the risk premium would require a ____ higher lower expected rate of return in the equity market.
higher
You aim to construct a portfolio of Apple and Microsoft that has a (target) return of 9.00%. The return on Apple (AAPL) is 12.5% and the return on Microsoft (MSFT) is 5.5%. What percentage of your portfolio should be allocated to MSFT stock now? (What is the weight on MSFT in your portfolio?) The solution can be obtained by solving a linear equation with one unknown (the portfolio weight).
hw 2 # 6
Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40 per share. She borrows $4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. a. What is the amount of margin (in dollars) in Dée's account when she first purchases the stock? b-1. If the share price falls to $30 per share by the end of the year, what is the remaining margin in her account? b-2. If the maintenance margin requirement is 30%, will she receive a margin call? c. What is the rate of return on her investment? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
hw 2 #11
You are bullish on Telecom stock. The current market price is $50 per share, and you have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of 8% per year and invest $10,000 in the stock. a. What will be your rate of return if the price of Telecom stock goes up by 10% during the next year? (Ignore the expected dividend.) b. How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately. (Round your answer to 2 decimal places.)
hw 2 #12
You've borrowed $20,000 on margin to buy shares in Ixnay, which is now selling at $40 per share. You invest 1,000 shares. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price changes to $35 per share. a. Will you receive a margin call? Yes No b. At what price will you receive a margin call?
hw 2 #13
Your portfolio consists of 2 shares of Apple stock (AAPL) and 1 share of Microsoft stock (MSFT). AAPL started at $192/share and ended at $216/share. MSFT started at $102/share and ended at $108/share. You want to calculate the return of your portfolio. Instead of using the weighted average of the returns on these two stocks, you consider an alternative method of calculating the return of a portfolio - namely, you treat the portfolio as a single asset. To this end, calculate the value of your portfolio at the start (see Example 1 in notes "lecs04-11-portfolioTheory-part1"), and then calculate the value of your portfolio at the end. Treat the portfolio as a single asset and calculate the return on your portfolio over this period of time using the formula: portfolio return = (portfolio value at the end - portfolio value at the start) / portfolio value at the start
hw 2 #2
Your portfolio consists of 2 shares of Apple stock (AAPL) and 1 share of Microsoft stock (MSFT). AAPL started at $204/share and ended at $216/share. MSFT started at $102/share and ended at $108/share. The weight of AAPL in your portfolio is 0.8 and the weight of MSFT is 0.2 (True/False)
hw 2 #3
Suppose you have $600 in your account. You bought 2 shares of Apple stock (AAPL) at $204/share and 1 share of Microsoft stock (MSFT) at $102/share. ___, the weight of MSFT is ____, and the weight of cash ____ The weight of AAPL in your portfolio is: The weight of MSFT in your portfolio is: The weight of Cash in your portfolio is:
hw 2 #4
The return on Apple (AAPL) is 12.5% and the return on Microsoft (MSFT) is 5.5%. If AAPL is 25% of your portfolio and MSFT is 75% of your portfolio, what is the return on your portfolio?
hw 2 #5 7.5%
Suppose you have $2,000 in your E*Trade account. You borrow $1,000 and invest all $3,000 in the Intel stock. Determine your portfolio weight Wintel and Wcash.
hw 2 #8
Suppose you have $2,000 in your E*Trade account. You sell short some Intel shares and receive $1500 in cash. Determine your portfolio weight Wintel and Wcash. Note that Intel's portfolio weight becomes negative after the short selling. You represent this position as follows:
hw 2 #9
risk free portfolio: expected return 10%, standard deviation 0% market portfolio: expected return 18%, standard deviation 24% portfolio A: expected return 20%, standard deviation 22% calculate the Sharpe ratios for the market portfolio and portfolio A if the CAPM is valid, is the situation possible?
market = (.18 - .10)/.24 = .33 A = (.20 - .10)/.22 = .45 if simple CAPM is valid, as the risk increases, the expected return on the portfolio also increases; in this case, market portfolio has a low return compared to portfolio A but market portfolio has a higher risk compared to portfolio A -> so this is NOT a valid case
If the simple CAPM is valid, is the following situation possible? portfolio A: expected return 20%, beta 1.4 portfolio B: expected return 25%, beta 1.2
no
risk free portfolio: expected return 10%, beta 0 market portfolio: expected return 18%, beta 1 portfolio A: expected return 16%, beta .9 Calculate the return predicted by CAPM for a portfolio with a beta of .9 What is the alpha of portfolio A? If the simple CAPM is valid, is the situation above possible?
return = .10 + .9(.18 - .10) = .172 alpha = .16 - .172 = -.012 no
risk free portfolio: expected return 10%, standard deviation 0 market portfolio: expected return 18%, standard deviation 1 portfolio A: expected return 16%, standard deviation 1.5 Calculate the the return predicted by CAPM for a portfolio with a beta of 1.5. What is the alpha of portfolio A? If the simple CAPM is valid, is the situation above possible?
return = .10 + 1.5(.18 - .10) = .22 alpha = E(r) - E(r CAPM) = .16 - .22 = -.06 no, the actual return of portfolio A is 16% less than its expected return; portfolio A will be below the security market line (alpha is -6%) -> portfolio is overvalued
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 20%. a. What is the investment proportion, y? b. What is the expected rate of return on the overall portfolio?
standard deviation = y * 27% y = (.20/.27) = .7407 = 74.07% mean return = .07 + (.17 - .07)y = .07 + .10(.7407) = .07 + .7407 = 14.41%
Consider a portfolio that is 60% (wS) in the S&P 500 index and 40% (wB) in the JPM bond index. Suppose an analyst estimates that E[rS] = 15%, σs = 20%, E[rB] = 10%, σB =12%, and ρ = 0% (the correlation coefficient is zero). 1) Calculate the portfolio's standard deviation given that the correlation is zero: 2) Calculate the weighted average of the standard deviations of the S&P 500 index and the JPM bond index:
standard deviation for a two-asset portfolio σp = (w12σ12 + w22σ22 + 2w1w2Cov1,2)1/2 w1 = weight of Asset 1 w2 = weight of Asset 2 σ12 = variance of Asset 1 σ22 = variance of Asset 2 Cov1,2 = covariance of returns between Asset 1 and Asset 2 Cov1,2 = ρ1,2 * σ1 * σ2, where ρ1,2 = correlation of returns between Asset 1 and Asset 2 standard deviation = ((0.60)2(0.20)2 + (0.40)2(0.12)2 + (2)(0.60)(0.40)(0)(0.20)(0.12))1/2 standard deviation = 12.92% weighted average of the standard deviations = (0.60 * 0.20) + (0.40 * 0.12) = 16.80%
according to the CAPM, the expected rate of return of a portfolio with a beta of 1 and an alpha of 0 is:
the expected return on the market
Stocks offer an expected rate of return of 10% with a standard deviation of 20%, and gold offers an expected return of 5% with a standard deviation of 25%. (LO 6-3) a. In light of the apparent inferiority of gold to stocks with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so. Note that (1) this question is similar to the example on whether or not to hold commodity together with stocks and bonds in lecture notes on applications of Markowitz's portfolio theory; (2) graphs for parts (a) and (b) are provided in the solutions to Problm 6-13 in Chapter 6 posted on Canvas. b. How would you answer (a) if the correlation coefficient between gold and stocks were 1? Draw a graph illustrating why one would or would not hold gold. Could these expected returns, standard deviations, and correlation represent an equilibrium for the security market? Answer: (a) Although it appears that gold is dominated by stocks, gold can still be an attractive diversification asset. If the correlation between gold and stocks is sufficiently low, gold will be held as a component in the optimal portfolio. (b) If gold had a perfectly positive correlation with stocks, gold would not be a part of efficient portfolios. The set of risk/return combinations of stocks and gold would plot as a straight line with a negative slope. The graph shows that he stock-only portfolio dominates any portfolio containing gold. This cannot be an equilibrium;the price of gold must fall and its expected return must rise.
true
What is the difference between a cash account and a margin (or cash-margin) account? A cash and margin account (or simply a margin account) allows the account holder to have an option (but not an obligation) to borrow money from the broker to buy securities. Owners of a cash account don't have such an option.
true -Cash account requires that all transactions must be made with available cash or long positions. Buying on margin occurs when an investor buys an asset by borrowing the balance from a bank or broker. --Buying on margin refers to the initial payment made to the broker for the asset—for example, 10% down and 90% financed. The investor uses the marginable securities in their broker account as collateral. The buying power an investor has in their brokerage account reflects the total dollar amount of purchases they can make with any margin capacity. Short sellers of stock use margin to trade shares.
If the simple CAPM is valid, is the following situation possible? portfolio A: expected return 30%, standard deviation 35% portfolio B: expected return 40%, standard deviation 25%
yes as long as A's beta is less than B's
Suppose instead that the fund was among the poorest performers in its comparison group. Would you be more or less likely to believe its relative performance will persist into the following year?
•more likely •the evidence is more suggestive of a tendency for poor performance to persist. This tendency is probably related to fund costs and turnover rates. Thus if the fund is among the poorest performers, investors would be concerned that the poor performance will persist.
Impressive Fund had excellent investment performance last year, with portfolio returns that placed it in the top 10% of all funds with the same investment policy. Do you expect it to be a top performer next year?
•no •empirical research indicates that past performance of mutual funds is not highly predictive of future performance, especially for better-performing funds. While there may be some tendency for the fund to be an above average performer next year, it is unlikely to once again be a top 10% performer.
