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.
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?
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
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.
clever.