Question

Consider the argument from the CAPM: “Stocks with beta larger than one are riskier, those with beta smaller than one are less risky.” Comment on the intuition of why this is the case. Show mechanically (mathematically) why this is the case.

Answer 1

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Question:

Answer:

CAPM Model:

This is a very popular and widely taken in use of stock valuation. CAPM means capital asset pricing model. CAPM model provide a formula by which an investor calculate the expected return on security based on its level of risk. Basically this model describe the relationship between systematic risk and expected rate of return. There are wo type of risk: First systematic risk and second is unsystematic risk. Systematic risk is related tho whole market or economy likes, risk related with change in GDP, AD, inflation, exchange rate etc. Unsystematic risk is related to specific security or industry like, change in company's fundamental, management, competition etc. Total risk is equal to systematic risk + unsystematic risk. Unsystematic risk can be diversifiable but systematic risk is not diversifiable.

Equation of CAPM Model:

R(e) = Rf + Beta (Rm- Rf)

Where,

R(e) = Required Return

Rf = Risk-free return

Rm = Market’s expected rate of return

Beta:

Beta measure the volatility in of a security or portfolio in comparison to the market as a whole. 0 beta means no volatility, 1 beta means security and market move in the same percentage like, if market grow 2% then that securities will grow the same and vice versa. If beta is more than 1 then it means security is more volatile like beta is 2 and market grow 3% then security will grow 6%. Beta is measure the systematic risk only.

Now understand the equation with an example:

Suppose,

R(e) = Required Return

Rf = 4%

Rm =7%

Beta = 2

R(e) = Rf + Beta (Rm- Rf)

R(e) = 4% + 2 (7%- 4%)

= 0.04 +2(0.07 - 0.04)

= 0.04 +2*0.03

= 0.1*100 = 10%

R(e) = 10%

Now suppose beta is 3

R(e) = Rf + Beta (Rm- Rf)

R(e) = 0.04 +3*0.03

= 0.13*100 = 13%

R(e) = 13%

So, we have seen than the required return is higher with the higher beta and vice- Veras because required higher return at higher risk and vice-versa. “Stocks with beta larger than one are riskier, those with beta smaller than one are less risky.”

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