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.作者: iteracom 时间: 2013-8-6 10:23
Given the usual way is to take
Is SR (Asset being added) > SR (Portfolio) * Correlation (Asset, Portfolio)
I am inclined to go with SR (Sharpe Ratio) - choice A.
C). Information Ratio = Active Return / Active Risk -> not applicable in this situation.
B) Treynor measure = (Rp - Rf) / Betap -> not applicable.作者: strikethree 时间: 2013-8-6 10:24
Typically opaque question , but I am going to assume “overall” means “total” , so A , Sharpe Ratio作者: Viceroy 时间: 2013-8-6 10:24
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 forget what the Treynor measure is.作者: liquidity 时间: 2013-8-6 10:24
Official ans from Qbank
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.作者: RMontgomery 时间: 2013-8-6 10:24
not sure where Schweese is doing its squeezing from.
I don’t recall where in the curriculum they talk about using Treynor to ever add Asset A to Portfolio B.
They do talk of Sharpe for that.
Are they saying
Treynor Portfolio < Treynor Asset -> go ahead and add…. need to see curriculum confirmation for that anywhere.作者: cfalevel2011 时间: 2013-8-6 10:24
the same thing could have been said with using Sharpe Portfolio * Correlation (Asset,Portfolio) < Sharpe Asset.
Can you give me the question id please?作者: pawn 时间: 2013-8-6 10:24
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.作者: Palantir 时间: 2013-8-6 10:24
Hahah well after that nice explanation you gave, I’m gonna say C is the right answer for this one.作者: brain_wash_your 时间: 2013-8-6 10:25
Correct nashwbe - C is it! With that happy note, let’s get out of work for some happy hour! TGIF.
When is all this going to get over, again, please remind me?作者: kickthatcfa 时间: 2013-8-6 10:25
For well-studied people such as yourself, this will be over in less than a month. For people like me, hopefully in 1 year + 1 month. : P作者: redskins44 时间: 2013-8-6 10:25
You don’t know how much under the water I am, mate… Just trying to drink it through! It’s slow poison.
I am taking this half a day off from study and get back to it probably Sat with GIPS (yes, I still have that pending)作者: Swanand 时间: 2013-8-6 10:25
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作者: busterbluth 时间: 2013-8-6 10:25
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.作者: thecfawannabe 时间: 2013-8-6 10:25
Analog of the first question: 1 is a positive number, but 1 is not a non-negative number.作者: thommo77 时间: 2013-8-6 10:25
Then why use the sharpe ratio ever when evaluating whether a stock should be added?作者: firat 时间: 2013-8-6 10:26
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.作者: DSquaredSlim 时间: 2013-8-6 10:26
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.作者: anshultongia 时间: 2013-8-6 10:26
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?作者: bulosehi 时间: 2013-8-6 10:26
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作者: smuggycfa 时间: 2013-8-6 10:26
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.作者: segalm 时间: 2013-8-6 10:26
Crucifier, this question is nasty broski. Where you get it?作者: mamuka12 时间: 2013-8-6 10:26
