Theme 40. Finance and the formation of an investment portfolio

r = Rf + beta (Rm – Rf) + Alpha
Therefore,
Alpha = R – Rf – beta (Rm-Rf)
Where:
R represents the portfolio return
Rf represents the risk-free rate of return
Beta represents the systematic risk of a portfolio
Rm represents the market return, per a benchmark


4.Practical use of CAPM method for the Analysis of investment portfolio


Task 6. Determine the expected rate of return for assets A and B using beta coefficient from CAPM model

We have the same financial data

Financial instruments	Expected rate of return, %	Population variance	Population standard deviation / risk	Sample variance	Sample standard deviation / risk
А	4,4	102,64	10,13	128,3	11,33
В	6,2	7,76	2,79	9,7	3,11
Index	5,8	43,76	6,62	54,7	7,4

In Microsoft Excel we can use formula “=ИНДЕКС(ЛИНЕЙН(массив 1;массив 2);1)”

We can calculate the beta of the asset A (with the Index)

β_А = = = 1,53

We can calculate the beta of the asset B (with the Index)

β_B = = = 0,37

Now, we can write the expected rate of return for assets A and B if the investor think that Index rate of return will be 15%. The risk-free rate is 3%:
The expected rate of return for the asset A from CAPM:

ER _A = R_f + β_A (ER_index – R_f) = 3 + 1,53 х (15 – 3) = 3 + 1,53 х 12 = 3 + 18,36 = 21,36%

You can compare it with the arithmetic average rate of return (mean) of the asset A – 4.4%.

The expected rate of return for the asset B from CAPM:

ER _B = R_f + β_B (ER_index – R_f) = 3 + 0,37 х (15 – 3) = 3 + 0,37 х 12 = 3 + 4,44 = 7,44%

You can compare it with the arithmetic average rate of return (mean) of the asset B – 6,2%.