SFM CAPM

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Swathi (Querist)
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02 August 2021 Hello,
Just came across this question but could not find the right answer.

You are given the following information about corporate stock P and the market:

Risk-free rate is 7

The expected return and volatility for corporate stock P is 7 and 33 respectively.
The Expected Return and Volatility for Market is 6 and 12 respectively.
The correlation between the returns of corporate stock P and the market is 18.
Assume the Capital Asset Pricing Model holds.
Calculate the required return for corporate stock P?
Could somebody solve it?
Thanks in advance.

Aashok Kumar Sharma online

Aashok Kumar Sharma online

(Expert)
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11 July 2024 To calculate the required return for corporate stock P using the Capital Asset Pricing Model (CAPM), we need to use the given information and the formula:

\[ R_P = R_f + \beta_P \times (R_M - R_f) \]

where:
- \( R_P \) is the required return for stock P,
- \( R_f \) is the risk-free rate,
- \( \beta_P \) is the beta of stock P,
- \( R_M \) is the expected return of the market.

Given:
- Risk-free rate (\( R_f \)) = 7%
- Expected return of corporate stock P (\( E(R_P) \)) = 7%
- Expected return of the market (\( R_M \)) = 6%
- Beta of stock P (\( \beta_P \)) = 1.8 (assuming correlation was intended to represent beta, which is common in practice even though the provided correlation value seems unusually high)

Now, let's calculate the required return \( R_P \):

1. Calculate the market risk premium (\( R_M - R_f \)):
\[ R_M - R_f = 6\% - 7\% = -1\% \]

2. Calculate the required return \( R_P \):
\[ R_P = 7\% + 1.8 \times (-1\%) \]
\[ R_P = 7\% - 1.8\% \]
\[ R_P = 5.2\% \]

Therefore, the required return for corporate stock P, according to the Capital Asset Pricing Model (CAPM), is \( \boxed{5.2\%} \).

This calculation assumes that the beta of stock P is correctly represented by the given correlation value of 1.8, which is unusual (betas typically range between -1 and 1). If the correlation value was intended to represent something else (such as a miscommunication), the calculation would need to be adjusted accordingly.

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