1. This document provides information on investments and bond pricing. It includes questions related to portfolio expected returns and risk given expected returns, standard deviations, and correlations of individual investments. 2. Questions ask to calculate portfolio expected returns and risk based on weights of investments in the portfolio and their correlations. Other questions calculate bond prices today given yield to maturity, coupon rates, time to maturity, and coupon payment frequencies. 3. The final questions calculate Treynor ratio and Jensen's alpha for portfolios with given returns, betas, market returns, and risk-free rates to evaluate portfolio performance relative to risk adjusted returns.

1. Practice Sheet-RMB FM-01
1. Consider the following investments:
Investmen
t Expected return
Standard
deviation
A 5% 10%
B 7% 11%
C 6% 12%
D 6% 10%
Which investment would you prefer between the following pairs?
a. A and D?
b. B and C?
c. C and D
2. The covariance of the returns on the two securities, A and B, is -0.0005. The standard
deviation of A's returns is 4% and the standard deviation of B's returns is 6%. What is the
correlation between the returns of A and B? (-0.2083)
3. Company X has a beta of 1.45. The expected risk-free rate of interest is 2.5% and the
expected return on the market as a whole is 10%. Using the CAPM, what is ABC’s
expected return? (13.375%)
4. ABC Company has a beta of 1.2. The expected risk-free rate of interest is 4% and the
expected premium for the market as a whole is 5%. What is the expected return for
ABC Company stock? (10%)
5. Consider Securities D and E with the following estimates:
E(RD) = 8% σD= 12% E(RE) = 13% σE = 20%
Now consider the portfolios that can be formed with D and E, assuming that the
investment is equal between D and E (that is, each has a weight of 50%). What is
the portfolio’s standard deviation if the correlation between D and E for each of the
following?
(a). 1 (b). 0.3 (c). 0 (d). -1 (16%,13%,11.6%,4%)
6. Consider Securities X and Y with the following
estimates: E(RX) = 5% σX= 10% E(RY) = 15%
σY = 25%
If the portfolio is comprise of 40% X and 60% Y and if the correlation between the
returns on X and Y is -0.25, what is the portfolio’s expected return and risk? (11%,
Risk-14.5268%)

2. 7. A bond has a face value of Rs.1000 with a time to maturity ten years from now.
The yield to maturity of the bond now is 10%.
a) What is the price of the bond today, if it pays no coupons? (Rs.385.54)
b) What is the price of the bond if it pays annual coupons of 10%? (Rs.1000)
c) What is the price today if pays 8% coupon rate semi-annually? (Rs.875.38)
8. a) What is the value today of a (Rs.1000 bond, 8% coupon with annual coupon
payments if the time to mature is 2 years and YTM is 4%? (Rs.1075.46)
b) What is the relationship between the yield and the price of a bond? Make a
graph of the values calculated above, with prices on the horizontal line and yields
on the vertical.
(9) If a portfolio has a return of 12% and a beta of 1.4, and if the risk-free rate is
2%, then what is its Treynor ratio? Also find out Treynor ratio if beta is 1.
(7.14,10)
(10) Calculate value of Jensen’s Alpha (1.6, 4, 5.2)
 portfolio return = 12%
 market return rate = 8%
 beta = 1.4,1,0.8
 risk-free rate = 2%