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How to calculate Portfolio Risk and Return?

Portfolio return: 
It is a return on portfolio earn by an investor or holder of an investment portfolio.  The return includes capital appreciation and dividend.

Formula of Portfolio return:
E(r)p = Æ©ni=1 wi *E(ri)
Where,
E(r)p = Expected return of a portfolio
Wi = weight of asset in a portfolio
E (ri) = expected return of a security or stock

Portfolio risk: It is a risk of losing return or decreasing the return of an investment due to certain factors. The higher return is expected by investors out of his investment but higher the return means higher the risk. Investors can decrease the risk by diversifying its investment.standard deviation helps to measure the volatility of expected return. Higher standard deviation means the investment is more risky.
Standard deviation = √ (probability (return – expected return) ^2)

Example: Calculate the expected return of a given portfolio of A and B:

Portfolio
Weight of stock
Return
A: i) AB stock
0.7
10%
ii) LM Stock
0.3
25%
B: i) PQ stock
0.5
15%
ii) MN stock
0.5
5%


Solution: 
Portfolio A:
E(r)p = Æ©ni=1 wi *E(ri)
= 0.7*10 + 0.3*25
= 7 + 7.5
= 14.5%
Portfolio B:
= 0.5*15 + 0.5*5
= 7.5 + 2.5
= 10%

Example: Mr. Verma has invested his 25%savings in stock A and 40% in stock B. The value of stock A is positively correlated with the market conditions. The stock value of B has an inverse relation with the market conditions. Find out the expected return.

State of economy
Stock
Probability
Return
Good
A
0.6
20%

B
0.4
10%
Bad
A
0.5
5%

B
0.5
25%

Solution:  Stock A:
= 0.6*20 + 0.5*5
= 12 + 2.5
= 14.5
Stock B:
= 0.4*10 + 0.5*25
= 4 + 12.5
= 16.5
Expected return of stock A:
= 0.25*14.5
= 3.625%
Expected return of stock B:
= 0.40*16.5
= 6.6%

Example: From the given information calculate portfolio variance:
Stock
State of economy
Probability
Return
A
Good
0.4
20%

Bad
0.6
45%

Solution: Expected return of stock A:
= probability (good market condition)* return + probability (bad market condition) * expected return
= 0.4*20 + 0.6*45
= 8 +27
= 35%
Standard deviation (σ) = √ (probability (return – expected return) ^2 )
= √ (0.4 (0.20 – 0.35) ^2 + 0.6 (0.45 – 0.35) ^2)
= √ (0.4*0.0225 + 0.6*0.01)
= √ (0.009 + 0.006)
=√ 0.015
= 0.122 or 12.2%

Example: Mr. Rohit has invested in 3 stocks A, B and C and the weights of each security in a portfolio are 30%, 20% and 10% respectively. Find out the portfolio return with the help of given information:

State of economy
Stock
Probability
Return
Good
A
0.3
32

B
0.4
9

C
0.3
15




Bad
A
0.3
19

B
0.5
16

C
0.2
12




Worst
A
0.5
10

B
0.3
4

C
0.2
8

Solution: Expected return of stock A:
 = 0.3*32 + 0.3*19 + 0.5*10
= 9.6 + 5.7 + 5
= 20.3%
Expected return of stock B:
= 0.4*9 + 0.5*16 + 0.3*4
=3.6 + 8 + 1.2
= 12.8%
Expected return of stock C:
= 0.3*15 + 0.2*12 + 0.2*8
= 4.5 + 2.4 + 1.6
= 8.5%
Expected return of portfolio:
= 0.3*20.3 + 0.2*12.8 + 0.1*8.5
= 6.09 + 2.56 + 0.85
= 9.5%



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