Skip to main content

What is Treynor Ratio?

Treynor Ratio: 
It measure the risk adjusted rate of return earned after considering the market risk. The ratio named after Jack L. Treynor. The ratio considers the systematic risk. It is same as Sharpe ratio but it consider beta not a standard deviation to measure the performance of an investment fund. Beta is sensitive to market conditions. Higher the ratios better the efficiency of an investment portfolio or fund.

Formula:
Treynor ratio = Rp – Rf / β
Where,
Rp = Expected return of a portfolio
Rf = Risk free rate of return
Β = Beta (systematic risk)

Advantages of Treynor ratio:
·         It helps to measure the performance of a fully diversified funds in which the unsystematic risk is zero.
·         It helps to rank the investment portfolio.

Disadvantages of Treynor ratio:
·         It does not consider total risk to measure the performance of a fund.
·         It is not suitable for undiversified portfolio.

Difference between Sharpe ratio and Treynor ratio:
·         Sharpe ratio considers standard deviation (total risk) to measure the efficiency of an investment fund while, Treynor ratio considers beta which is sensitive to market movements.
·         Sharpe ratio is used when the portfolio is not fully diversified while the Treynor ratio is used when the portfolio is fully diversified.

Example: Calculate the Treynor ratio with the help of given information:
·         The expected return of a Portfolio A is 12.3% and risk free rate is 4%.
·         The beta is 2.15.
Solution:
Treynor ratio = Rp – Rf / β
= 12.3 – 4 / 2.15
= 3.86%

Example: Find out which investment asset provides excess return after considering the systematic risk factor with the help of treynor ratio.
·         The expected return of stock A is 8.6% and risk free rate of return is 2.6%. The beta of market is 1.18.
·         The expected return of stock L is 9.8% and risk free rate of return is 1.36%. The beta is -1.32.
·         The expected return of P stock is 10.5% and the risk free rate is 1.5%. The beta is 0.45%
·         The expected return of stock C is 14.3% and the risk free rate of return is 3.12%. The beta coefficient is 2.32.

Solution: Treynor ratio = Rp – Rf / β
Stock A:  8.6 – 2.6 / 1.18 = 5.08%
Stock L: 9.8 – 1.36 / -1.32 = -6.39%
Stock P: 10.5 - 1.5 / 0.45 = 20%
Stock C: 14.3 – 3.12 / 2.32 = 4.81%
The stock P has higher Treynor ratio. So, it is better for the investment.

Example: Mr. Mehta wants to invest in any one of the following stock which gives excess return over risk free rate. He wants to consider all the risk associated with the stocks. Find out which investment gives better return if the market risk is high.

Investment
Expected return
Beta
Standard deviation
A
9.2%
0.23
29%
B
9.0%
1.56
19%
C
10.6%
1.45
22%
 The risk free rate of all three stocks is 3%.

Solution:
Investment
Treynor ratio = Rp – Rf / β
Sharpe ratio =Rp – Rf / σ
A
= 9.2 – 3 / 0.23 = 26.96%
= 9.2 – 3 / 29 = 0.21%
B
= 9.0 – 3 / 1.56 = 3.85%
= 9.0 – 3 / 19 = 0.32%
C
= 10.6 – 3 / 1.45 = 5.24%
= 10.6 – 3 / 22 = 0.35%


The Treynor ratio shows that stock A is better for investment and the Sharpe ratio shows that stock C is better for investment. Mr. Mehta wants to consider all the risk associated with the stocks. So, the stock C is best for him. If he consider the market risk only then Stock A is best for him.

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