INVESTMENT ANALYSIS – CALCULATION OF BETA, ALPHAS, SML ETC

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Below is the complete workings of the question I posted earlier. 

BETA

The beta is used to measure the underversifiable  risk of an asset.  That is, it is used to measure the systematic risk of an asset. We all know we have two systematic and unsystematic risk.

The formula for Beta:

b= R₂ – R₁

    M₂ – M₁

 Where:

R₂ = Return on individual security

M₂ = Return on the portfolio

ILLUSTRATION:

Consider the following data which gives a security analyst expected return on two stocks for two particular market returns.

Market Return	Aggressive Stock	Defensive Stock
5%	-2%	6%
25%	38%	12%

1. What are the Betas of the two stocks?
2. What is the expected Return on each stock if the market return is equally likely to be 5% or 25%?
3. If the risk free Rate of Return is 6% and the market return is equally likely to be 5% or 25%, what is the SML?
4. What are the Alphas of the two stocks ?
5. Which stock is undervalued and which stock is overvalued?

             

SOLUTION:

First of all, we have to determine the beta of the Aggressive Stock before the Defensive stock.

Here we go:

 b= R₂ – R₁

    M₂ – M₁

b= 38-( –2)

      25-5

Explanation:  Do you know how we got 38? 38 is R2, which is the aggressive stock figure row2, while -2 is the aggressive stock figure in row1.

Then 25% is the market rate of return in row2 while 5 is the market rate of return in row 1.  Please look at the formula again.

So let continue:

b= 40

     20

Don’t ask me how I got the 40 above, because minus multiply by minus  gives you plus.

b= 2

Our beta for Aggressive stock is 2.

Now with that we can solve for Defensive.  It is the same procedure:

Defensive Stock:

b= R₂ – R₁

    M₂ – M₁

b= 12-6

      25-5

b=    6

      20

b=    0.3

Our Defensive stock is 0.3

Solution to (B) of the question:

What is the expected Return on each stock if the market return is equally likely to be 5% or 25%. That is the question:

Here is the formula for Expected Return.

Ṝ = ∑(R.P)

Note, we are solving for Aggressive Stock first.

Ṝ = (-2x0.5) + 38 x 0.5

Ṝ = -1 + 19

Ṝ = 18%

The Expected return for Aggressive Stock is 18: Remember, when the weight or probability of a security is not given, then we assumed is 50% 50%. That is how we got 0.5.

So, let’s solve for Defensive stock:  It is the same procedure:

Ṝ = (6x0.5) + 12 x 0.5

Ṝ = 3 + 6

Ṝ = 9%

Now for Solution (c):

Security Market Line (SML) equation:

SML: E(R) = Rf + (E(Rm) – Rf) b

E(R) 6+ (15 – 6) b

E(R) 6+ (9) b

The answer to C is: E(R) 6+ (9) b

Solution to (d) To determine the Alphas:

Here is the formula of Alphas:

Alpha ( a)=E(R:) – Rf + (E(Rm)-Rf) b

Now we are solving for Aggressive Stock:

a =18 – (6+(9)2

a =18 – 6+18

a =18 – 24

a =6%

6% is the alphas of Aggressive Stock:

Now we are solving for Defensive Stock:

a =9 – (6+(9)0.3

a =9 – 6+(2.7)

a =9-8.7

a =0.3

0.3 is the alphas of Defensive stock.

Now let’s solve for question E:

Which stock is undervalued and which stock overvalued?

The solution to E:

Aggressive is overvalued because the expected return is less than the required return i.e. 18< 24

Defensive stock is undervalued because the expected rate of return is greater than the required rate of return i.e. 9 >8.7