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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.

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