Performance Measurement Q particular, comparing, determine, addition, adjusted

burning0spear

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.

mamuka12

So what’s the consensus here Crucifier?

segalm

Crucifier, this question is nasty broski. Where you get it?

smuggycfa

Here’s a disturbing counter point for the schweez:
consider the Singer-Terhaar approach for defining the risk premium of an asset class in integrated markets
RP(ac) = Std Dev(ac) * Corr(ac,GIM) * [RP(GIM) / Std Dev(GIM)]
where RP = Risk Premium or R - Rf; and GIM = Global Investable Market
rearranging this formula and expanding we have:
[R(ac) - Rf] / Std Dev(ac) = [R(GIM) - Rf] / Std Dev(GIM) * Corr(ac,GIM)
or rather Sharpe(ac) = Sharpe(GIM) * Corr(ac,GIM)
Now the GIM is certainly a diversified portfolio so why can we use the sharpe ratio in this situation? By Schweser’s rationale the ratio used should have been the Treynor ratio.
If I am wrong someone please explain it to me, but I think Schweser may have taken to many assumptions in thier conclusion to this answer.

bulosehi

I agree with Fin,
If portfolio is well diversified, there will be nearly no difference before and after you add one more stock.
so Treynor is same, Sharpe is same
IR also same and nearly 0

anshultongia

I see what they are getting at, but I don’t think it’s as simple as they are trying to make it. I would like to know the answer to CPK’s question of: are they saying if Treynor (Port)
Normally (if using the Sharpe) you would need to account for correlation between the portfolio and the new asset, but correlation is a function of std dev (total risk) so you couldn’t use correaltion of assets and portfolios when using the Treynor. Instead you would need to compare the relation between betas of the two assets, which would be a totally different measure.
Most portfolios are diversified (at least that’s the goal of many portfolios) so why would CFAI focus on using the Sharpe when adding new securities to portfolios?

DSquaredSlim

For a well diversified portfolio. the two measures(sharpe ratio and treynor ratio) should give the same conclusion. Adding the stock will have impact on the beta and the unssytematic risk, although it may be insignificant.

firat

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.

thommo77

Then why use the sharpe ratio ever when evaluating whether a stock should be added?

thecfawannabe

Analog of the first question: 1 is a positive number, but 1 is not a non-negative number.