Skip to main content

What is Arbitrage Pricing Theory?

Arbitrage Pricing Theory: 
It is developed by Stephen Ross in 1976. It is a linear model and used for estimating the asset price. It helps to determine the assets are overvalued or undervalued. With the help of arbitrage investors can make a profit through price differences of asset without any investment. There are many macro economic factors (like inflation) and market and security specific factors which affect the price of an assets and it is difficult  to determine which factor consider or which should not. There are some factors which affect the price of security like-
·         Inflation
·         Gross Domestic Product
·         Interest rate
·         Market index
·         Investors confidence
·         Shift of yield curve etc.
      To calculate the expected return on stock you have to consider these factors which affect the price of that stock. 
If alpha is greater than zero then the expected return is greater it means the security is overpriced. And if alpha is smaller than zero it means expected return is smaller and security is under priced.

Arbitrage: It is an activity in which any investor can buy a security from one market and simultaneously sell it to other market for making risk less profit through price discrimination of same security. The person who engages in this buying and selling activity is known as arbitrager.

Formula:
E(r)i = rf + βi1 RP1 + βi2 RP2 + βi3 RP3 +.... βin RPn + ei
Where,
E(r)i = expected rate of return
rf = risk free rate
βi = beta sensitive to the associated factor
RP = risk premium
Ei= error term (unsystematic risk)
Assumptions:
·         All investors have homogeneous interest.
·         There is no arbitrage and if it is exist then the investors take the advantages of it and turned into equilibrium state.
·         It has no transaction cost, no tax.

Advantages:
·         It includes more than one factor which affects the price of security.
·         With the help of it determine the Is the security overprice or under priced?
·         It helps to make arbitrage free market.

Disadvantages:
·         It does not specify the factors which affect the price of the security.
·         It is difficult to identify the factors which affect the price of security and expected rate of return.

Example: Find out the expected return of portfolio A if the beta of portfolio is 1.52 and risk free rate is 2%. Through research it has been analysed that there are 2 factors which affect the portfolio A most is Inflation and interest rate. The beta of inflation is 0.96 and risk premium is 5%. The beta and risk premium of interest rate is 2.12 and 3% respectively.

Solution:
E(r)i = rf + βi1 RP1 + βi2 RP2 + βi3 RP3 +.... βin RPn + ei
= 2 + 0.96 + 5 + 2.12 + 3
= 13.08%

Example: Using the arbitrage pricing theory find out the expected return if the risk free rate is 2% from the following information:

Security
Factor
Beta (β1)
factor
Beta (β2)
A
2.33
2.10
0.98
0.78
B
1.3
1.26
1.25
1.95
C
0.65
1.45
2.56
0.89

Solution:
E(r)i = rf + βi1 f1 + βi2 f2 + βi3 f3 +.... βin fn + ei
Security
A
B
C
Calculation
=2.1*2.33 + 0.78*0.98
= 4.90+0.76
= 5.66
= 1.26*1.3+ 1.95*1.25
=1.64+2.44
=4.08
= 1.45*0.65+ 0.89*2.56
=0.94+2.28
=3.22






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...
Post a Comment
Read more