FINE 3200 Lecture Notes - Lecture 4: Arsenic, Sharpe Ratio, Standard Deviation

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23 May 2017

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The expected cash flow is (. 5 ,000) + (. 5 200,000) = ,000. With a risk premium of 8 percent over the risk-free rate of 6 percent, the required rate of return is 14 percent. Therefore, the present value of the portfolio is. ,000/1. 14 = ,421: if the portfolio is purchased for ,421, and provides an expected cash inflow of ,000, then the expected rate of return [e(r)] is derived as follows: The portfolio price is set to equate the expected rate of return with the required rate of return: if the risk premium over t-bills is now 12 percent, then the required return is. The present value of the portfolio is now. ,000/1. 18 = ,407: for a given expected cash flow, portfolios that command greater risk premiums must sell at lower prices. The extra discount from expected value is a penalty for risk.

Related Questions

1. The Treasury bill rate is 4percent, and the expected return on the market portfolio is 12percent. Using the capital asset pricing model:

b. What is the risk premium on the market?
c. What is the required return on an investment with a beta of1.5?
d. If an investment with a beta of .8 offers an expected return of9.8 percent does it have a positive NPV?
e. If the market expect a return of 11.2 percent from Stock X, whatis its beta?

2. Percival Hygiene has $10 million invested in long-term corporatebonds. This bonds portfolios expected annual rate of return is 9percent and annual standard deviation is 10 percent.
Amanda Reckcon with, Percival's financial adviser recommends thatPercival consider investing in an index fund which closely tracksthe Standard and Poor's 500 index.

a.Suppose Percival put all his money in a combination of index fundand treasury bills. Can he thereby improve his expected rate ofreturn without changing the risk of portfolio . The treasury billyield is 6 percent.
b.Could Percival do even better by investing equal amount in thecorporate bond portfolio and the index fund? The correlationbetween the bond portfolio and the index fund is + 1.

beigegoose437

1. If we are able to eliminate all of the unsystematic or diversifiable risk in a portfolio then, what is the result?

a.

a risk-free portfolio
b.
a portfolio that has an expected return of zero
c.

a portfolio that contains only systematic risk

2. A portfolio consists 20% of a risk-free asset and 80% of a stock. The risk-free return is 4%. The stock has an expected return of 15% and a standard deviation of 30%. Whatâs the expected return of the portfolio?

a.
9.5%
b.
15.0%
c.
12.8%

d.
2%

3. The risk-free rate is 5% and the expected return on the market portfolio is 13%. A stock has a beta of 1.5, what is its expected return?

a.
12%
b.
19.5%
c.

17%

4. For what value of the correlation coefficient for the returns of a pair of stocks will the benefits of diversification the largest?

a.

1.0
b.

-1.0
c.

0.0
d.

0.5

5. Which of the following is an example of systematic risk?
a.
IBM posts lower than expected earnings.
b.
The overall stock market becomes more risky due to super fasting trading algorithms.
c.

Intel announces record earnings.

6. According to the CAPM (capital asset pricing model), the security market line is a straight line. The intercept of this line should be equal to

a.
zero
b.
the expected risk premium on the market portfolio
c.
the expected return on the market portfolio
d.
the risk-free rate

7. A portfolio has 40% invested in Asset 1, 50% invested in Asset 2 and 10% invested in Asset 3. Asset 1 has a beta of 1.2, Asset 2 has a beta of 0.8 and Asset 3 has a beta of 1.8, whatâs the beta of the portfolio?

a.
0.80
b.
1.06
c.
1.27

8. Suppose you can borrow and lend at the risk free-rate of 3%. Which of the following four risky portfolios has the best return relative to risk. (Hint: Calculate Sharpe Ratios the ratio of risk premium to standard deviation for each portfolio)

a.
portfolio with a standard deviation of 15% and an expected return of 12%
b.
portfolio with a standard deviation of 12% and an expected return of 9%
c.
portfolio with a standard deviation of 25% and an expected return of 18%
d.
portfolio with a standard deviation of 19% and an expected return of 15%

9. Which statements are TRUE regarding risk and return?

Statement I:
Diversification is the process of removing systematic risk from a portfolio.
Statement II:
In general, the greater the risk, the greater the return required by an investor.
Statement III:
Investors should focus on real returns if they are concerned about the purchasing power of their wealth.

a.
Statements II and III only
b.
Statement I only
c.
Statements I and III only
d.
Statements I and II only

10. The beta of the risk-free asset is:
a.

1.0
b.

0.5
c.

0.0
d.

-1.0

1. You own a stock portfolio invested 15 percent in Stock Q, 20 percent in Stock R, 35 percent in Stock S, and 30 percent in Stock T. The betas for these four stocks are 1.1, 0.8, 1.2, and 0.9, respectively. What is the portfolio beta? (Round your answer to 3 decimal places.)

2. You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.95, and the total portfolio is exactly as risky as the market, what must the beta be for the other stock in your portfolio? (Round your answer to 2 decimal places.)

Beta
3. A share of stock sells for $38 today. The beta of the stock is 1, and the expected return on the market is 17 percent. The stock is expected to pay a dividend of $1.10 in one year. If the risk-free rate is 3.7 percent, what should the share price be in one year? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Share price

4. A stock has a beta of 0.7 and an expected return of 9 percent. A risk-free asset currently earns 4 percent.

a.	What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Expected return

b.	If a portfolio of the two assets has a beta of 0.6, what are the portfolio weights?(Round your answers to 2 decimal places. Omit the "%" sign in your response.)

	Weight
x_S	%
x_rf	%

c.	If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Round your answer to 2 decimal places.)

Beta

d.	If a portfolio of the two assets has a beta of 2.80, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Omit the "%" sign in your response.)

	Weight
x_S	%
x_rf	%

5. Asset W has an expected return of 8 percent and a beta of 2. If the risk-free rate is 5.5 percent, what is the market risk premium? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Market risk premium

6. Stock Y has a beta of 1.5 and an expected return of 12 percent. Stock Z has a beta of 0.8 and an expected return of 8 percent. What would the risk-free rate have to be for the two stocks to be correctly priced relative to each other? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Risk-free rate

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FINE 3200 Lecture Notes - Lecture 4: Arsenic, Sharpe Ratio, Standard Deviation

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