Skip to main content

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%



Comments

Post a Comment

Popular posts from this blog

How to calculate Cost of Preference Share Capital?

Cost of Preference Share Capital:  An amount paid by company as dividend to preference shareholder is known as Cost of Preference Share Capital. Preference share is a small unit of a company’s capital which bears fixed rate of dividend and holder of it gets dividend when company earn profit. Dividend payable is not a tax deductible amount. So, there is no tax adjustments required for comparing with cost of debt. Formula for Cost of Preference Share: Irredeemable Preference Share Redeemable Preference Share K p  = Dp/NP K p  = D p +((RV-NP)/n )/ (RV+NP)/2 Where, K p  = Cost of Preference Share D p  = Dividend on preference share NP = Net proceeds from issue of preference share (Issue price – Flotation cost) RV = Redemption Value N = Period of preference share Example:  A company issues 20,000 irredeemable preference share at 8% whose face value is Rs.50 each at 4% discount. Find out the Cost of ...
88 comments
Read more

What is the difference between Cheque book and Pass book?

 Cheque book is issued by bank in customers / account holder request. With the help of this book account holder can withdraw cash from his/her account. Bank does not charge any fee to issued cheque book to its customer. But afterward bank charges some amount for using bank facility like cheque book, Debit card etc.So, Automatic some definite amount deducted from customer bank account. Pass book is  also issued by bank to its customer. It helps to record all the bank related activity according to date that is withdrawal and deposit. It is recorded by bank but the book is kept by customer to know the current balance of  his /her account.  Point of difference Pass book Cheque book What is the meaning of pass book and cheque book? Passbook is a book in which all withdrawal and deposit against customer account is recorded.   Cheque book is a book of cheques which are used to withdrawal the money to b...
Post a Comment
Read more

Numericals with solutions of Net income Approach

Net income approach questions and answers:   Questions:  Find out the value of the firm with the help of given information: Particulars Amount Earnings before interest and tax 3, 50, 000 Cost of equity 10% Cost of debt 7.2% Debenture 1,00,000 Find out the overall cost of capital with the help of net income approach. (Assume tax rate-10%) Solution: Particulars Amount Earnings before interest and tax 3, 50, 000 Less: Interest @7.2% 7, 200 Earnings before tax 3, 42, 800 Less: Tax@10% 34, 280 Net income 3, 08, 520 Cost of equity 10% Market value of equity (S =net income/ cost of equity) 30, 85, 200 Market value of debt (B) 1, 00, 000 Value of the firm (S+B) 31, 85, 200 Questions:  Find out the overall cost of capital if the equity capitalisation rate is 12...
1 comment
Read more