Question

State of market	Probability	HPR
Boom	.22	52.5%
Normal growth	.30	18.5
Recession	.48	-17.5

1. Compute the expected return and standard deviation of the HPR

2. Calculate the expected return and standard deviation of a complete portfolio invested 40% on risky assets. If risk free rate is 4%.

2-Suppose the nominal interest rate is 7% per year and the expected inflation rate is 3%. What is the real interest rate?

3- Calculate the geometric average for the following rates of return 10%, 15,20 ,-5, and 1%

Answer 1

1-a) Calculation of expected return and standard deviation of HPR :

• Expected Return (Mean Return) =( Probability * Expected Return according to the state of economy)
• Standard Deviation =

1-b) Calculation of expected return and standard deviation of a portfolio :

• Expected Return = (Weight of Security 1 * Return of Security 1) + (Weight of Security 2 * Return of Security 2)

= (0.40*8.7) + (0.60*4)

= 5.88%

• Standard Deviation of Portfolio ()=

Standard Deviation of Risk Free Asset is 0. Hence, Covariance between risky asset and risk free asset is will also be 0.

Therefore:

Weight of Security 1 (W1) = 0.40

Weight of Security 1 (W2) = 0.60

Standard Deviation of Risky Asset () = 27.93

Standard Deviation of Risky Free Asset () = 27.93

Covariance(1,2) = 0

=

=

=11.17397

2) Calculation of real interest rate :

• 1 + Nominal Rate = (1 + Real Rate) * (1+ Inflation Rate)

1+ 0.07 = (1+ Real Rate) * (1+0.03)

1.07 = (1+ Real Rate) * 1.03

By Switching sides :

(1+ Real Rate) * 1.03 = 1.07

1+ Real Rate = 1.07/1.03

Real Rate = 1.038835-1

Real Rate = 0.038835 i.e, 3.88% (approx.)