finc exam 2 chp4-6

The Vanguard 500 Index Fund tracks the performance of the S&P 500. To do so, the fund buys shares in each S&P 500 company

proportion to the market value weight of the firm's equity in the S&P 500

Assume that you have just purchased some shares in an investment company reporting $500 million in assets, $50 million in liabilities, and 50 million shares outstanding. What is the net asset value (NAV) of these shares?

$9 NAV = ($500 - $50)/50 = $9

Which risk can be partially or fully diversified away as additional securities are added to a portfolio? I. Total risk II. Systematic risk III. Firm-specific risk

1 and 3

An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20%, while the standard deviation on stock B is 15%. The correlation coefficient between the returns on A and B is 0%. The rate of return for stocks A and B is 20 and 10 respectively. The expected return on the minimum-variance portfolio is approximately _________.

13.6%

Consider a mutual fund with $300 million in assets at the start of the year and 12 million shares outstanding. If the gross return on assets is 18% and the total expense ratio is 2% of the year-end value, what is the rate of return on the fund?

15.64% 300000000(1.18)=354000000 .02*3540000000=7080000 (354000000-7080000-300000000)/300000000=15.64%

Suppose you pay $9,700 for a $10,000 par Treasury bill maturing in 3 months. What is the holding-period return for this investment?

3.09%

Your investment has a 20% chance of earning a 30% rate of return, a 50% chance of earning a 10% rate of return, and a 30% chance of losing 6%. What is your expected return on this investment?

9.2%

The geometric average of -12%, 20%, and 25% is

9.7%

Rank the following from highest average historical return to lowest average historical return from 1926 to 2013. I. Small stocks II. Long-term bonds III. Large stocks IV. T-bills

I, III, II, IV

You are considering investing in one of several mutual funds. All the funds under consideration have various combinations of front-end and back-end loads and/or 12b-1 fees. The longer you plan on remaining in the fund you choose, the more likely you will prefer a fund with a __________ rather than a __________, everything else equal.

front-end load; 12b-1 fee

Advantages of investment companies to investors include all but which one of the following?

guaranteed rates of return

Decreasing the number of stocks in a portfolio from 50 to 10 would likely _

increase the unsystematic risk of the portfolio

Which of the following ETFs tracks the S&P 500 Index?

spiders

To construct a riskless portfolio using two risky stocks, one would need to find two stocks with a correlation coefficient of ________.

-1.0

You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. Your HPR was ____.

11%

An investment earns 10% the first year, earns 15% the second year, and loses 12% the third year. The total compound return over the 3 years was

11.32%

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. & A 1 percentage point decrease in the risk-free rate. A 1 percentage point increase in expected return and 1 percentage point decrease in the risk-free rate will have the same impact of increasing Sharpe ratio from .40 to .45

-----funds stand ready to redeem or issue shares at their net asset value.

Open-end

The Investments Fund sells Class A shares with a front-end load of 6% and Class B shares with 12b-1 fees of .5% annually as well as back-end load fees that start at 5% and fall by 1% for each full year the investor holds the portfolio (until the fifth year). Assume the portfolio rate of return net of operating expenses is 10% annually. a. If you plan to sell the fund after four years, are Class A or Class B shares the better choice for you? b. What if you plan to sell after 15 years?

a. Suppose you have $1000 to invest. The initial investment in Class A shares is $940 net of the front-end load. After 4 years, your portfolio will be worth: $940 × (1.10)^4 = $1,376.25 Class B shares allow you to invest the full $1,000, but your investment performance net of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you sell after 4 years. Your portfolio value after 4 years will be: $1,000 × (1.095)^4 = $1,437.66 After paying the back-end load fee, your portfolio value will be: $1,437.66 × 0.99 = $1,423.28 Class B shares are the better choice if your horizon is 4 years. b. With a 15-year horizon, the Class A shares will be worth: $940 × (1.10)^15 = $3,926.61 For the Class B shares, there is no back-end load in this case since the horizon is greater than 5 years. Therefore, the value of the Class B shares will be: $1,000 × (1.095)^15 = $3,901.32 At this longer horizon, Class B shares are no longer the better choice. The effect of Class B's 0.5% 12b-1 fees cumulates over time and finally overwhelms the 6% load charged to Class A investors.

Consider the following table: Scenario Probability Stock Fund Rate of Return Bond Fund Rate of Return Severe recession .10 -37% -9% Mild recession .20 -11% 15% Normal growth .35 14% 8% Boom .35 30% -5% a. Calculate the values of mean return and variance for the stock fund. b. Calculate the value of the covariance between the stock and bond funds.

a. Mean return 9.5 % Variance .0454 b. covariance -0.0043

According to Tobin's separation property, portfolio choice can be separated into two independent tasks consisting of __________ and __________.

identifying the optimal risky portfolio; constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion

Suppose your expectations regarding the stock market are as follows: State of the Economy Probability HPR Boom 0.3 44% Normal growth 0.4 14 Recession 0.3 -16 Use above equations to compute the mean and standard deviation of the HPR on stocks. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

mean: 14% standard deviation: ?? not 5.4%

The primary measurement unit used for assessing the value of one's stake in an investment company is

net asset value

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 for the equity fund?

portfolio risk premium/std dev of portfolio excess return 10%/14%=.71

The ______ measure of returns ignores compounding.

arithmetic average

Mutual funds that hold both equities and fixed-income securities in relatively stable proportions are called

balanced funds

A measure of the riskiness of an asset held in isolation is ____________.

standard deviation

An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20%, while the standard deviation on stock B is 15%. The correlation coefficient between the returns on A and B is 0%. The standard deviation of return on the minimum-variance portfolio is _________.

12%

The market risk premium is defined as

the difference between the return on an index fund and the return on Treasury bills

Many current and retired Enron Corp. employees had their 401k retirement accounts wiped out when Enron collapsed because ________.

their 401k accounts were not well diversified

Risk that can be eliminated through diversification is called ______ risk.

unique firm-specific diversifiable XXall of these options

Consider a no-load mutual fund with $200 million in assets and 10 million shares at the start of the year and with $250 million in assets and 11 million shares at the end of the year. During the year investors have received income distributions of $2 per share and capital gain distributions of $.25 per share. Assuming that the fund carries no debt, and that the total expense ratio is 1%, what is the rate of return on the fund?

23.75% NAV0 = $200/10 = $20.00 NAV1 = [$250 - ($250 × .01)]/11 = $22.50 Gross return = ($22.50 - $20 + $2 + $.25)/$20 = 23.75%

Your investment has a 40% chance of earning a 15% rate of return, a 50% chance of earning a 10% rate of return, and a 10% chance of losing 3%. What is the standard deviation of this investment?

5.14%

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?

Expected return for your fund = T-bill rate + risk premium = 6% + 10% = 16% a. Expected return of client's overall portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% b. Standard deviation of client's overall portfolio = 0.6 × 14% = 8.4%

The composition of the Fingroup Fund portfolio is as follows: Stock SharesPrice A 230,000 $40 B. 330,000 $45 C. 430,000 $20 D. 630,000 $25 The fund has not borrowed any funds, but its accrued management fee with the portfolio manager currently totals $30,000. There are 5 million shares outstanding. What is the net asset value of the fund? (Round your answer to 2 decimal places.)

Given that net asset value equals assets minus liabilities expressed on a per-share basis, we first add up the value of the shares to get the market value of the portfolio: StockValue Held by Fund A$9,200,000 B 14,850,000 C 8,600,000 D 15,750,000 Total$48,400,000 Knowing that the accrued management fee, which adjusts the value of the portfolio, totals $30,000, and the number of the shares outstanding is 5,000,000, we can use the NAV equation: Net asset value =(Market value of assets − Market value of liabilities)/Shares outstanding = $48,400,000 − $30,000/5,000,000= $9.67

Corporate Fund started the year with a net asset value of $13.70. By year-end, its NAV equaled $12.70. The fund paid year-end distributions of income and capital gains of $2.00. What was the rate of return to an investor in the fund?

Given the NAV at the beginning and the end of the period, and the distributions during the period, we can use the equation below to solve for the rate of return of the Corporate Fund: Rate of return =(Δ(NAV) + Distributions)/ Start of year NAV =(-$1.00 + $2.00)/$13.7 = 0.0730 = 7.30%

Based on the outcomes in the following table, choose which of the statements below is (are) correct? I. The covariance of security A and security B is zero.II. The correlation coefficient between securities A and C is negative.III. The correlation coefficient between securities B and C is positive.

I and II only

Suppose you've estimated that the fifth-percentile value at risk of a portfolio is −30%. Now you wish to estimate the portfolio's first-percentile VaR (the value below which lie 1% of the returns). Will the 1% VaR be greater or less than −30%?

The 1% VaR will be less than -30%.

The rate of return on _____ is known at the beginning of the holding period, while the rate of return on ____ is not known until the end of the holding period.

Treasury bills; risky assets

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? 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 (S) of your risky portfolio and your client's overall portfolio?

a. Allocating 70% of the capital in the risky portfolio P, and 30% in risk-free asset, the client has an expected return on the complete portfolio calculated by adding up the expected return of the risky proportion (y) and the expected return of the proportion (1 − y) of the risk-free investment: E(rC) = y × E(rP) + (1 − y) × rf = (0.7 × 0.17) + (0.3 × 0.07) = 0.14 or 14% per year. The standard deviation of the portfolio equals the standard deviation of the risky fund times the fraction of the complete portfolio invested in the risky fund: σC = y × σP = 0.7 × 0.27 = 0.189 or 18.9% per year b. The investment proportions of the client's overall portfolio can be calculated by the proportion of risky portfolio in the complete portfolio times the proportion allocated in each stock. Security InvestmentProportions T-Bills =30.0% Stock A 0.7 × 27% =18.9% Stock B 0.7 × 33% =23.1% Stock C 0.7 × 40% =28.0% c. We calculate the reward-to-variability ratio (Sharpe ratio) using Equation 5.14. For the risky portfolio: (.17-.07)/.27=.03704 (.14-.07)/.189=.3704

The Closed Fund is a closed-end investment company with a portfolio currently worth $285 million. It has liabilities of $3 million and 5 million shares outstanding. a. What is the NAV of the fund? b. If the fund sells for $53 per share, what is its premium or discount as a percent of NAV? (Input the amount as a positive value. Round your answer to 2 decimal places.)

a. NAV =(Market value of assets - Market value of liabilities)/Shares outstanding = $285,000,000 - $3,000,000/5,000,000= $56.40 b. Premium (or discount) = (Price - NAV)/NAV = ($53 - $56.40)/56.4 = -0.0603 = -6.03%

City Street Fund has a portfolio of $502 million and liabilities of $12 million. a. If there are 49 million shares outstanding, what is net asset value? b-1. If a large investor redeems 2 million shares, what happens to the portfolio value? (Enter your answer in millions.) b-2. If a large investor redeems 2 million shares, what happens to shares outstanding? (Enter your answer in millions.) b-3. If a large investor redeems 2 million shares, what is net asset value?

a. NAV =Market value of assets − Market value of liabilitiesShares outstanding = ($502,000,000 − $12,000,000)/49,000,000= $10 b. Because 1 million shares are redeemed at NAV = $10, the value of the portfolio decreases to: Portfolio value = $502 million - ($10 × 2 million) = $482 million The number of shares outstanding will be the current shares outstanding minus the number of shares redeemed: 49 million - 2 million = 47 million. Thus, net asset value after the redemption will be: NAV =(Market value of assets − Market value of liabilities)/Shares outstanding = ($482,000,000 − $12,000,000)/47,000,000= $10

Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rƒ. The characteristics of two of the stocks are as follows: Stock expected return std dev a 8% 40% b 13% 60% correlation=-1 a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be substituted for the risk-free asset?) b. Could the equilibrium rƒ be greater than 10%?

a. Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio in equilibrium will always be the risk-free rate. To find the proportions of this portfolio [with wA invested in Stock A and wB = (1 - wA) invested in Stock B], set the standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation reduces to: σP = ABS[wAσA - wBσB] 0 = 40wA - 60(1 - wA) ⇒⇒ wA = .60 The expected rate of return on this risk-free portfolio is: E(r) = (.60 × 8) + (.40 × 13) = 10.0% b. No E(r) = 10.0% Therefore, the risk-free rate must also be 10.0%.

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 15% 32% Bond fund (B) 9% 23% The correlation between the fund returns is 0.15. a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%? b. Calculate the standard deviation of the portfolio which yields an expected return of 12%.

a. Using only the stock and bond funds to achieve a mean of 12%, we solve: 12 = 15wS + 9(1 − wS ) = 9 + 6wS ⇒⇒ wS = .5 = 50% b. From the standard deviations and the correlation coefficient we generate the covariance matrix [note that Cov(rS, rB) = ρσSσB]: Bonds Stocks 529.0 110.4 110.4 1,024.0 Investing 50% in stocks and 50% in bonds yields a mean of 12% and standard deviation of: σP = [(0.502 × 1,024) + (0.502 × 529) + (2 × 0.50 × 0.50 × 110.4)] 1/2 = 21.06% The efficient portfolio with a mean of 12% has a standard deviation of only 21.06%. Using the CAL reduces the standard deviation by 45 basis points.

Your assistant gives you the following diagram as the efficient frontier of the group of stocks you asked him to analyze. The diagram looks a bit odd, but your assistant insists he double-checked his analysis. a. would you trust him? b. is it possible to get such a diagram?

a. No, it is not possible to get such a diagram. Even if the correlation between A and B were 1.0, the frontier would be a straight line connecting A and B.