Question

ci. You have been provided the following data on three securities and the market portfolio. Beta 1.5 Observed (Realized) Return 15.0% 12.0% 10.0% 10.0% 5.0% Security/Portfolio Security 1 Security 2 Security 3 Market portfolio Riskfree security Standard Deviation 01 18.0% 2.0% 4.0% 0.0% Correlation 1.0 0.4 P3, m B2 0.5 Pin, m Bm Pem BE Note that the return in the above table is the average realized return on security j. Assume the CAPM is correct and that the market portfolio and the riskfree security are correctly priced. a) Fill the missing values of the table. Show your calculations where appropriate.

Answer 1

Beta =systematic risk / market risk

systematic risk=SD of security(SD_i) * correlation between security and market

Security1: Syetematic risk=SD₁ * Correlation

=SD₁*1

=SD₁

Beta=SD₁/.04

1.5=SD₁/.04

SD₁=1.5*.04

=.06 or 6%

Security2: Systamic risk=18*.4=7.2%

Beta=7.2/4 =1.8 (note we can take sd in either % term or in numbers but same way shoud be followed both in numerator and denominator)

Security3: .5=2*Correlation/4

.5*4=2*Correlation

Correlation=2/2

=1