# Essentials of Investment Assignment

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1a.A municipal bond carries a coupon rate of 7% and is trading at par. What would be the equivalent taxable yield of this bond to a taxpayer in a 40% tax bracket?

b. A municipal bond carries a coupon rate of 7% and is trading at par. A corporate bond pays a rate of 10%. At what marginal tax rate would an investor be indifferent between these two bonds?

2. Consider the three stocks in the following table. Pt represents price at time t, and Q t represents shares outstanding at time t.

Stock C

splits three- for- one in the last period.

P0 Q0 P1 Q1 P2 Q2

A 80 200 90 200 90 200

B 50 300 40 300 40 300

C 90 200 110 200 40 600

a. Calculate the rate of return on a price- weighted index of the three stocks for the first period (t=0 to t=1)

b. What must happen to the divisor for the price- weighted index in year 2?

c. Calculate the rate of return of the price-weighted index for the second period (t=1 to t=2)

3. The current market price for Google stock is \$800 per share and you have \$40,000 of your own money. Suppose your broker’s initial margin requirements is 50% of the value of the position and maintenance margin is 30% of the value of the position.

a. What is your maximum possible loss if you short Google at \$800?

b. Suppose you are bullish on Google and buy 100 share of Google at \$800 per share. How long can the price of the stock drop before you get a margin call if the maintenance margin is 30% of the value of the short position?

c. Suppose you are bearish on Google and short 100 share of Google at \$800 per share. How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position?

4a. If the offering price of an open-end fund is \$14 per share and the fund is sold with a front-end load of 6%, what is its net asset value?

b. If an open-end fund as a net asset value of \$11 per share and the fund is sold with a front-end load of 6%. What is the offering price?

5. You are a portfolio manager or a risky portfolio with an expected rate of return of 15% and a standard deviation of 20%. The

T-bill

rate is 5%. Suppose your risky portfolio includes the following investments in the given proportions.

Stock Given Proportions

Stock A

20%

Stock B

30%

Stock C 50%

Suppose your client decides to invest in your risky portfolio a proportion of (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 13%

a. What is the proportion of y?

b. What is the standard deviation of the rate of return on your client’s portfolio?

c. What are your client’s investment proportions in your three stocks and the T-bill fund?

Proportion

T-bill
Stock A
Stock B
Stock C

d. Suppose your client is wondering if he should switch his money in your fund to a passive portfolio invested to mimic the S&P500 stock index yields an expected rate of return of 11% with a standard deviation of 18% Show your client a maximum fee you could charge (as a percent of the investment in your fund deducted at the end of the year) that would still leave him at least as well off investing in your fund as in the passive one. (Hint: The fee will lower the slope of your client’s CAL by reducing the expected return net of the fee.)

6. There are three mutual funds available in the market. 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 6%. The probability distribution of the risky funds are:

Expected Return

Standard Deviation

Stock fund (S) 20% 30%

Stock fund (B) 10 22

*The correlation between the fund returns is .2

a. What are the expected return and standard-deviation of the minimum-variance portfolio?

b. What is the reward-to-volatility ratio of minimum-variance portfolio?

7. Assume CAPM is valid. Please answer the following questions. Consider each situation independently.

Table A

Portfolio Expected Return Beta

A 25% 1.8

B 30 1.1

a. Is the situation in Table A possible? Briefly explain.

Table B

Portfolio Expected Return Standard Deviation

Risk free 5% 0%

Market 15 14

A 16 16

b. Is the situation in table B possible? Briefly explain.

Table C

Portfolio Expected Return Beta

Risk free 10% 0

Market 18 1.0

A 16 1.5

c. Is the situation in table C possible? Briefly explain.

d. Is the Stock A in Table C under-valued or over-valued?