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1. What are financial intermediaries, and what economic functions do they perfor

ID: 2677058 • Letter: 1

Question

1. What are financial intermediaries, and what economic functions do they perform?

2. The real risk-free rate of interest is 3 percent. Inflation is expected to be 2 percent this year and 4 percent during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?

3. Interest rates on 1-year Treasury securities are currently 5.6 percent, while 2-year Treasury securities are yielding 6 percent. If the pure expectations theory is correct, what does the market believe will be the yield on 1-year securities 1 year from now?

4. The probability distribution of a less risky expected return is more peaked than that of a riskier return. What shape would the probability distribution have for (a) completely certain returns and (b) completely uncertain returns?

5. Security A has an expected return of 7 percent, a standard deviation of expected returns of 35 percent, a correlation coefficient with the market of 0.3, and a beta coefficient of 1.5. Security B has an expected rate of return of 12 percent, a standard deviation of returns of 10 percent, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?

6. Assume that the risk-free rate is 5 percent and the market risk premium is 6 percent. What is the expected return for the overall stock market? What is the required rate of return on a stock that has a beta of 1.2?

7. Assume that the risk-free rate is 6 percent and the expected return on the market is 13 percent. What is the required rate of return on a stock that has a beta of 0.7?

Explanation / Answer

1. What are financial intermediaries, and what economic functions do they perform?

Solution:

Financial intermediaries may include

-      banks,

-      broker-dealers,

-      investment advisers and

-      Financial planners.

The functions performed by financial intermediaries are:-

-      Converting risky investments into relatively risk-free ones

-      Converting short-term liabilities to long term assets

-      Matching small deposits with large loans and large deposits with small loans.

2. The real risk-free rate of interest is 3 percent. Inflation is expected to be 2 percent this year and 4 percent during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?

Solution:


Given that r* = 3%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0;

We have to find rT2 =? ; rT3 =?

r = r* + IP + DRP + LP + MRP.

Since these are Treasury securities, DRP = LP = 0.

rT2 = r* + IP2.

IP2 = (2% + 4%)/2

IP2 = 3%.

rT2 = 3% + 3%

rT2 = 6%

rT3 = r* + IP3.

IP3 = (2% + 4% + 4%)/3

IP3 = 3.33%.

rT3 = 3% + 3.33%

rT3 = 6.33%

3. Interest rates on 1-year Treasury securities are currently 5.6 percent, while 2-year Treasury securities are yielding 6 percent. If the pure expectations theory is correct, what does the market believe will be the yield on 1-year securities 1 year from now?

Solution:

Let X equals the yield on 1-year securities 1 year from now:

(1.056)1(1 + X) 1 = (1.06)2

(1.056) (1 + X) = 1.1236

1 + X = 1.1236/1.056

1 + X = 1.064

X = 1.064 – 1

X = 0.064

X = 6.4 %.

4. The probability distribution of a less risky expected return is more peaked than that of a riskier return. What shape would the probability distribution have for (a) completely certain returns and (b) completely uncertain returns?

Solution:


a. completely certain return - Since there is no variability in returns, the probability distribution curve for certain return would be straight line. b. Completely uncertain return – Since there is no variability in returns, the probability distribution curve for certain of returns, the shape of probability distribution curve would be a horizontal line.

5. Security A has an expected return of 7 percent, a standard deviation of expected returns of 35 percent, a correlation coefficient with the market of – 0.3, and a beta coefficient of – 1.5. Security B has an expected rate of return of 12 percent, a standard deviation of returns of 10 percent, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?

Solution 5:

If it was a case of diversified portfolio security A would have been less risky because of its negative correlation with other stocks. On the other hand in a single-asset portfolio, security A would have been more risky as compared to security B because s a > s b and CV a > CV b.

6. Assume that the risk-free rate is 5 percent and the market risk premium is 6 percent. What is the expected return for the overall stock market? What is the required rate of return on a stock that has a beta of 1.2?

Solution:

Given that Risk free rate = 5%,

Market risk premium = 6% and

Beta = 1.2

Required return on stock,

                                          = 5 + 1.2*6

                                          = 5 + 7.2

                                           = 12.2%

7. Assume that the risk-free rate is 6 percent and the expected return on the market is 13 percent. What is the required rate of return on a stock that has a beta of 0.7?

Solution:

Given that Risk free rate = 6%,

Expected return on market = 13% and

Beta = 0.7

Required return on stock,

                                          = 6 + 0.7 (13 – 6)

                                           = 6 + 0.7*7

                                            = 6 + 4.9

                                            = 10.9%