A portfolio manager has a well diversified portfolio and they are trying to determine whether or not to add a particular stock to the portfolio to increase the portfolio’s overall risk adjusted return. To decide whether or not to add the stock the manager will back test the portfolio based on historical data of the stock and the portfolio. The relevant measure to use in comparing the results of the back tested model comparing the results of the portfolio before and after the addition of the stock would be the:
A) Sharpe ratio. B) Treynor measure. C) Information ratio.
Agreed, I would say choice A for the same reason cpk mentioned. The traditional way to see if it’s worth adding a stock to a portfolio is to compare the Sharpe ratio of the asset being added to the Sharpe ratio of the existing portfolio (multiplied by its correlation to the stock). So Sharpe Ratio is most relevant.
Info ratio isn’t relevant in my opinion, agreed with cpk.
I fell for the exact same trap, wrote the same formula out.
Alas, the ans is B, becase they gave in the question that it’s already a well diversified fund and so Treynor makes more sense to figure out the risk-adjusted-return than Sharpe
The goal is to add a greater return to the portfolio without appreciably increasing the level of risk. Since the portfolio is already well diversified most of its risk is related to systematic risk (beta) which is the relevant measure of risk in the denominator of the Treynor measure. Adding one risky stock to an already diversified portfolio will not appreciably change the overall risk of the portfolio thus beta and the Treynor measure remain the relevant measures used to compare the results of the portfolio with and without the addition of the stock. The Sharpe ratio uses standard deviation in the denominator of the equation. Standard deviation is comprised of systematic risk (beta) and unsystematic risk. If the portfolio was not well diversified then most of the risk would be unsystematic or company specific risk. Adding one stock to an undiversified portfolio would most likely still leave a lot of unsystematic risk thus making standard deviation and the Sharpe ratio the relevant measures if the portfolio was undiversified. The information ratio is used to compare the return to a benchmark which is not a concern to the portfolio manager in this question.
I think I need a good/long break. Good luck forks, see you tomorrow with a fresh mind.
Which of the following measures would be the most appropriate one to use when comparing the results of two portfolios in which each portfolio contains only a few number of stocks representing a limited number of industries?
A) Treynor measure. B) Information ratio. C) Sharpe ratio.
Haha nice man, I feel slightly better since you seem to know a lot. If it makes you feel better, I’m going to start “managed futures” for the first time after work today. I wish I could say I was starting on GIPS. : P
If it is a well diversified portfolio then wouldn’t std dev result is a similar value as beta? well diversified means only systematic risks remain in the potfolio and unsystematic risks=0
Std dev = systematic + unsystematic of 0 = systematic only remains
Beta = systematic only
so Sharpe and Treynor would produce the same conclusion in this case.
Based on the explanation provided, the Sharpe of the stock being added is not equal to the Treynor of the stock since the stock exhibits unsystematic risk. The diversified portfolio, on the other hand, should not be affected by which ratio is used, for the reason you gave. But when the stock is added, unsystematic risk will be diversified away, so why use the Sharpe ratio when looking at the stock’s contribution to the portfolio? I think that’s why Treynor is best here.
Check out the 2nd question provided by L3Crucifier in this thread - that’s when you would use Sharpe. Since the portfolio that the stock will be added to is not diversified, then the new stock’s unsystematic risk is actually going to significantly contribute to total risk. As a result, you should look at the relative Sharpes to see if the reward for total risk is worth it.
If the portfolio is diversified, the reward for total risk is irrelevant. All that matters is reward for systematic risk, since the stock’s unsystematic risk will have an insignificant effect on the diversified portfolio.