Investments Midterm

The standard deviation of return on investment A is 11%, while the standard deviation of return on investment B is 6%. If the correlation coefficient between the returns on A and B is −0.152, the covariance of returns on A and B is _________

-0.001

A $500,000 stock portfolio has an annual expected return of 12% and a standard deviation of 35%. What is the portfolio VaR at a 5% probability level?

0.12 + 0.35(z 5%) = -45.57% VAR: -227850

The standard deviation of return on investment A is 23%, while the standard deviation of return on investment B is 18%. If the covariance of returns on A and B is 0.008, the correlation coefficient between the returns on A and B is __________.

0.193

Asset A has an expected return of 36% and a standard deviation of 40%. The risk-free rate is 14%. What is the reward-to-variability ratio?

0.55

.A portfolio with a 25% standard deviation generated a return of 20% last year when T-bills were paying 4.0%. This portfolio had a Sharpe ratio of __________.

0.64

A stock quote indicates a stock price of $100 and a dividend yield of 3%. The latest quarterly dividend received by stock investors must have been ______ per share.

0.75

Suppose the risk premium of the market portfolio is 8% and the beta of company D is 1.2. You also consider adding a stock Z to your portfolio, which has beta of 0.8. 1. What is the expected rate of return for stock D if T-bill rate is 3%? 2. What is the expected rate of return for portfolio that consist of 60% of D and 40% of Z?

1. 12.6% 2. 11.32

Investors short 100 shares of X at $60 per share using 50% margin account. She has $3,000 in T-bills for cover her margin position. 1. What is the initial account value before short? 2. What is the initial equity position? 3. What is the equity position and margin if price goes up to $70? 4. What is the equity position and margin if price goes up to $50? 5. What should be the price of X before the investor get a margin call (30%)?

1. t-bill: 3000 equity: 3000 2. t-bill: 3000 cash: 6000 | short: 6000 equity: 3000 3. e=2000, m=28.57%, 4. e=4000, ret=33.33 5. $69.23

You have a $41,000 portfolio consisting of Intel, GE, and Con Edison. You put $22,800 in Intel, $8,400 in GE, and the rest in Con Edison. Intel, GE, and Con Edison have betas of 1.3, 1, and 0.8, respectively. What is your portfolio beta

1.119

You put up $75 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $4.50. Your HPR was __________.

10%

Consider the capital asset pricing model. The market degree of risk aversion, A, is 3. The market variance is 2.25%. If the risk-free rate of return is 4%, the expected return on the market portfolio

10.75%

Pioneers' Fund is a closed-end investment company with a portfolio currently worth $320 million. It has liabilities of $4 million and 8 million shares outstanding. If the fund sells for $35 a share, what is its premium or discount as a percent of NAV?

11.39%

An investment earns 50% the first year, earns 55% the second year, and loses 52% the third year. The total compound return over the 3 years was __________.

11.60%

You invest in a mutual fund that charges a 4% front-end load, 2% total annual fees, and a 3% back-end load, which decreases 0.5% per year. How much will you pay in fees on a $10,100 investment that does not grow if you cash out after 3 years of no gain?

1111.99

.Consider a no-load mutual fund with $390 million in assets and 15 million shares at the start of the year and with $440 million in assets and 16 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 $0.30 per share. Assuming that the fund carries no debt, and that the total expense ratio is 2%, what is the rate of return on the fund?

12.5%

According to the CAPM, what is the expected market return given an expected return on a security of 17.2%, a stock beta of 1.6, and a risk-free interest rate of 6%?

13%

What is the HPR for a share of stock that was purchased for $25, sold for $27 and distributed $1.25 in dividends?

13%

NorthEast Airlines has a market beta of 1.2 and T-bond beta of 0.7. Suppose the risk premium of the market index is 6%, while that of the T-bond portfolio is 3%. Then the overall risk premium on NorthEast stocks is the sum of the risk premiums required as compensation for each source of systematic risk. Calculate the expected return of NorthEast Airlines if the risk-free rate

13.3%

The risk premium for exposure to aluminum commodity prices is 4%, and the firm has a beta relative to aluminum commodity prices of 0.6. The risk premium for exposure to GDP changes is 6%, and the firm has a beta relative to GDP of 1.2. If the risk-free rate is 4%, what is the expected return on this stock?

13.6%

Consider the multifactor APT with two factors. Portfolio A has a beta of 0.5 on factor 1 and a beta of 1.25 on factor 2. The risk premiums on the factor 1 and 2 portfolios are 1% and 7%, respectively. The risk-free rate of return is 7%. The expected return on portfolio A is __________ if no arbitrage opportunities exist.

16.25%

4.You short-sell 600 shares of Tuckerton Trading Company, now selling for $30 per share. What is your maximum possible gain, ignoring transactions cost?

18000

You consider buying a share of stock at a price of $13. The stock is expected to pay a dividend of $1.42 next year, and your advisory service tells you that you can expect to sell the stock in 1 year for $16. The stock's beta is 1.8, rf is 14%, and E[rm] = 24%. What is the stock's abnormal return?

2%

The variance of the return on the market portfolio is 0.04 and the expected return on the market portfolio is 20%. If the risk-free rate of return is 10%, the market degree of risk aversion, A, is __________.

2.5

Consider the CAPM. The risk-free rate is 3%, and the expected return on the market is 12%. What is the expected return on a stock with a beta of 1.9

20.1

On a given day a stock dealer maintains a bid price of $1,005.00 for a bond and an ask price of $1,007.50. The dealer made 16 trades that totaled 800 bonds traded that day. What was the dealer's gross trading profit for this security?

2000

An open-end fund has a NAV of $21.00 per share. The fund charges a 6% load. What is the offering price?

22.34

A mutual fund has total assets outstanding of $79 million. During the year the fund bought and sold assets equal to $19.75 million. This fund's turnover rate was _____.

25%

A project has a 50% chance of doubling your investment in 1 year and a 50% chance of losing half your money. What is the expected return on this investment project

25%

You are considering investing $2,500 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 75% and 25% respectively. X has an expected rate of return of 18%, and Y has an expected rate of return of 14%. To form a complete portfolio with an expected rate of return of 8%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y, respectively

25%, 19%, 6%

Security A has a historical rate of return of 12% and a beta of 1.1. The market expected rate of return is 8%, and the risk-free rate is 5%. The alpha of the stock is __________.

3.7%

You find that the bid and ask prices for a stock are $13.75 and $15.05, respectively. If you purchase or sell the stock, you must pay a flat commission of $20. If you buy 300 shares of the stock and immediately sell them, what is your total implied and actual transaction cost in dollars?

430

You short-sell 200 shares of Rock Creek Fly Fishing Company, now selling for $30 per share. If you want to limit your loss to $2,945, you should place a stop-buy order at ___.

44.73

Assume that you have just purchased some shares in an investment company reporting $240 million in assets, $40 million in liabilities, and 40 million shares outstanding. What is the net asset value (NAV) of these shares?

5

An investor purchases one municipal bond and one corporate bond that pay rates of return of 5% and 6.4%, respectively. If the investor is in the 15% tax bracket, his after-tax rates of return on the municipal and corporate bonds would be, respectively, _____.

5% 5.44%

4.You invest $1,500 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 7%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 10%.

50%

What is the tax exempt equivalent yield on a 9% bond yield given a marginal tax rate of 26%?

6.66%

Assume you purchased 500 shares of XYZ common stock on margin at $50 per share from your broker. If the initial margin is 75%, the amount you borrowed from the broker is _________.`

6250

The Chompers Index is a price weighted stock index based on the 3 largest fast food chains (divisor 3.0). The stock prices for the three stocks are $84, $38, and $74. What is the price weighted index value of the Chompers Index?

65.33

According to the CAPM, what is the market risk premium given an expected return on a security of 18.7%, a stock beta of 1.3, and a risk-free interest rate of 7%?

9%

You are considering investing in a no-load mutual fund with an annual expense ratio of 0.9% and an annual 12b-1 fee of 1.05%. You could also invest in a bank CD paying 7.5% per year. What minimum annual rate of return must the fund earn to make you better off in the fund than in the CD?

9.45%

A T-bill quote sheet has 90-day T-bill quotes with a 5.36 ask and a 5.41 bid. If the bill has a $10,000 face value, an investor could sell this bill for _____.

9864.75

An investor purchases 90-day T-bill for $9,875. Find discount, bond equivalent yield, and effective annual yield of this investment.

Discount: 5% bond equivalent: 5.13% effective annual: 5.23%

Suppose the risk-free rate is 5%, the average risk aversion A hat is 2, volatility of the market is 20%. Estimate the expected market return.

Erm 13%

Recession: prob: 0.2, HPR= -10%, var= -14.1 Normal Growth: prob: 0.5, HPR= 5%, var= 0.9 Boom: prob: 0.3, HPR= 12%, var= 7.9

Erp = 4.1% var p = 7.67%

recession: prob: 0.10, S: -22%, B: 30% below avg: prob: 0.10, S: -2%, B: 15% avg: prob: 0.40, S: 20%, B: 0% above avg: prob: 0.20, S: 35%, B: -10% boom: prob: 0.10, S: 50%, B: -20%

Ers: 17.4% var s: 20% var b: 13.76% var p: 3%

Suppose you buy a 10,000 T-bill maturing in 6 months for $9,900. On the bill's maturity date, you collect the face value. Find HPR (6 months), APR, EAR?

HPR: 1.1% APR: 2.2% EAR: 2.03%

Stock A: Shares: 370000, Price: 35 Stock B: Shares: 470000, Price: 40 Stock C: Shares: 570000, Price: 10 Stock D: Shares: 770000, Price: 15 If during the year the portfolio manager sells all of the holdings of stock D and replaces it with 210,000 shares of stock E at $40 per share and 210,000 shares of stock F at $15 per share, what is the portfolio turnover rate? If D shares originally were purchased at $11.50. What are the tax implication for the Fingroup Investors? Assume long-term capital gains and the average AGI below $500,000.

Profit: 2695000 tax impact: 404200

An index consists of the following securities and has an index divisor of 2.0. What are the price-weighted, value-weighted, and equal-weighted index returns? Stock A: #shares: 3000, Beginning Price: $44, End Price: $46 Stock B: #shares: 2800, Beginning Price: $32, End Price: $31

R pw = 1.32% R vw = 1.44% R ew = 0.71%

Buy a share of stock for $50, hold for 1 year, collect $1 dividend, and sell stock for $54. What were dividend yield, capital gains yield, and total return?

Total Yield: 10% Dividend Yield: 2% CG yield: 8%

You decided to invest $100 in a mutual fund that charges a 10% front-end load and a 5% back-end load. It is expected to deliver 20% annual performance over the next 3 years. How much you will get after the end of the 3rd year? Compare it to passive index investment with no fees and 15% annualized return?

active: 147.74 passive: 152.10

Stock A has a historical return of 10% and a beta of 1.2. The expected market rate of return is 9% and the risk-free rate is 5%. Find the abnormal performance of these stocks using CAPM.

alpha 0.2%

monthly HPR of 1%. find apr and ear

apr: 12% ear: 12.68%

Investors pays $35,000 towards the purchase of the 70,000 worth of stock (1,000 shares at $70 per share), borrowing the remaining 35,000 from a broker. What is the initial margin? What is the new margin if price drops to $60? What is the lowest price before the margin call?

initial: 50% new margin: 41.6% lowest price: 58.33 vs 60

Assume that you invested $100 in the fund that that grew to $105 at the end of the first year, $115.5 at the end of the second year, and 109.73 at the end of the third year. The fund did not pay any dividends or capital gains. Find average arithmetic, geometric, dollar-weighted returns.

ra: 3.33% rg: 3.1% rdw: 3.36%

Current 1-year Treasury rate is 4.10% and the inflation is 8.2%. What is the current real rate? Assume that inflation increases to 10%, what should happen to the nominal rate?

real rate: -3.79% nom rate: 5.8%

4.You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 14%. The stock and bond portfolios have a correlation of 0.55. The standard deviation of the resulting portfolio will be

var = .169

You need to choose between investing in a one-year municipal bond with a 8 percent yield and a one-year corporate with similar characteristics. If your marginal federal income tax rate is 32 percent and no other differences exist between these two securities. What is the yield of the corporate bond? What is the tax-adjustment premium?

yield: 11.74% Premium: 3.74%