Nyenrode Business Universiteit
Answers of study exercises
Risk and the Required Rate of Return
© Nyenrode Center for Finance - Dennis Vink
1
Risk and the Required Rate of Return
1. The standard deviation of the market portfolio is 4%. The risky asset S shows a
correlation coefficient with the market of 0.75 and a standard deviation of 8%.
Compute the beta of asset S.
Answer:
β
s = [ 8 * 4 * 0.75 ] / 16 = 1.5
2. The beta of the market portfolio itself is 1. Why?
Answer:
The correlation of the market with the market is of course 1, so:
σ
m*
σ
m*1 /
σ
²m = 1
3. The stock of an important food retail company has a beta of 1.2. The expected
return on the market portfolio is 12% and the risk-free rate 6%. What is the
expected or required rate of return on that stock?
Answer:
E (rfrc) = 6% + (12% - 6%) * 1.2 = 13.2%
4. The standard deviation of the market portfolio described in problem 3 is 4%. That
of the stock of the food retailer is 8%. How can you explain this, given
the beta of 1.2? Hint: draw a CML (Capital Market Line) and a SML (Security Market
Line) on the same scale next to each other and compare the two.
Answer:
Determine the correlation coefficient =>
β
= 1.2 = ( 4 % * 8 % *
ρ
)/ 16 =>
ρ
= 0.6.
The systematic risk is 0.6 * 8% = 1.2 * 4% = 4.8%, being
ρ
jm*
σ
j or
β
jm *
σ
m.
