# Calculating stock and portfolio beta

There are two stocks, stock A and stock B. The price of stock A today is $70. The price of stock A next year will be $50 if the economy is in recession, $80 if the economy is normal and $95 if the economy is expanding. The attendant probabilities of recession, normal times, and expansion are 0.2, 0.6, 0.2, respectively. Stock A pays no dividend. Assume the CAPM is true. Other information about the market includes:

SD(Rm)= Standard deviation of the market portfolio = 0.10

SD(Rb)= Standard deviation of stock B's return = 0.12

Rb= Expected return on stock B = 0.10

Corr(Ra,Rm)= The correlation of stock A and the market = 0.7

Corr(Rb,Rm)= The correlation of stock B and the market = 0.34

Corr(Ra,Rb)= The correlation of stock A and stock B = 0.6

What is the beta of the portfolio consisting of 30% of stock A and 70% of stock B?

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#### Solution Preview

Please refer attached file for better clarity of tables and formulas.

Solution:

Stock A

State of economy Probability Price Return*

P R P*R P*(R-Mean)^2

Recession 0.2 50 -0.28571 -0.05714285 0.029755102

Normal 0.6 80 0.14286 ...

#### Solution Summary

Solution describes the steps to calculate beta of stock A and B with the help of statistics given. It also calculates beta of portfolio consisting of stock A and stock B.