I have read through the explanation many times and I am still not sure why we do not use Portfolio 5 to calculate adjacent Corner Portfolios. In Example 9 (the BlueBox right before this question) we clearly used the two adjacent corner portfolios. In texample 10, they use one of the risky portfolios above the required rate of 6.5% and the risk-free rate. Why the risk-free rate? The case clearly says that “Exhibit 19 gives results from the sign-constrained MVO based on the inputs in Exhibit 18.” IF it is sign-constrained that means no shorting is allowed so why do they use the risk-free rate and omit Portfolio 5?
The solution says “Note that we need not consider the portion of the efficient frontier beginning at and extending below Corner Portfolio 5, because the portfolios on it do not satisfy CEFA’s 6.5 percent return objective”. The whole point of mixing two corner portfolios is to BLEND them in order to get the most mean-optimized average portfolio given a return requirement. We did the same thing in Example 9.
I even worked out the weights of Corner Portfolio 4 and 5’s standard deviations and the combined weighted value is still under the 12% standard deviation.
Can someone please have a look at this and tell me what I am missing? Did something miraculously change from Example 9 to Example 10?
A trustee has suggested that CEFA adopt the sole objective of minimizing the level of standard deviation of return subject to meeting its return objective.
given that - using the risk free asset with the minimum variance portfolio (highest sharpe ratio) would be the one.
1.CEFA’s portfolio should be structured to maintain diversification levels that are consistent with prudent investment practices.
2.CEFA has a capacity to accept a standard deviation of return of 12 percent or less.
3.CEFA’s portfolio should be constructed with consideration of minimizing the probability that the annual portfolio return will fall below CEFA’s spending rate.
In Example 9, Part 1A, the recommended strategic asset allocation was an efficient portfolio that was expected to just meet the return objective. With different capital market expectations and risk-free rates, however, that will not always be the case. For example, the expected return of the highest-Sharpe-ratio efficient portfolio (the tangency portfolio) may exceed the return objective, and if so, it may be optimal for the investor to hold the highest-Sharpe-ratio efficient portfolio in combination with the risk-free asset (as suggested in a capital allocation line analysis). On the other hand, as in Example 10, the highest-Sharpe-ratio efficient portfolio’s expected return may be below the return objective. Assuming that margin is not allowed, in such cases the highest-Sharpe-ratio portfolio is not optimal for the investor.
Cpk is right. A trustee has suggested that CEFA adopt the sole objective of minimizing the level of standard deviation of return subject to meeting its return objective To minimize risk without lowering the Sharpe ratio, we can combine the tangency portfolio with T-bills to choose a portfolio on CEFA’s capital allocation line. (We would lower the Sharpe ratio if we combined Corner Portfolio 4 with Corner Portfolio 5.)
This is no doubt a confusing couple of questions, here’s how I look at it. The objectives are:
1.) Maximise returns for level of risk taken. This means the Sharpe ratio needs to be maximised given all other objectives are met.
2.) 6.5% return is required
3.) Standard deviation of no more than 12%
Let’s go straight to the tangency portfolio (4) as it will have the highest Sharpe ratio. It meets both return and risk objectives, so is a good pick. The only way to improve given the constraint of objective 1 is to combine it with the risk free asset, as this will not decrease the Sharpe ratio (as it’s on the CAL).
We now need to choose between portfolio 4 and P4 with risk free asset. As suggested in the text, we use Roy’s safety first measure. The winner here is portfolio 4, so we go with that.
I’m unsure on Q2, would combining P4 and P5 give a lowed SD than combining P4 with the risk free asset? Correlations aren’t 1 so we can’t use a weighted average method to calculate standard deviation.
Thanks for your input everyone. This is certainly one of those bespoke, customized questions where a few lines really define the entire thinking process: "A trustee has suggested that CEFA adopt the sole objective of minimizing the level of standard deviation of return subject to meeting its return objective."
I have two follow up questions:
First Question:
In the curriculum, in a small paragraph right before Example 10 it says that the best way to maximizing risk-adjusted returns without reducing the Sharpe ratio is to use the RF asset. This is very important. IS this primarily why they chose to mix CP 4 with the RF asset?
Second Question:
In light of this and Matt’s understanding, I think there are 3 possible scenarios that they might throw at us. Can you all please confirm or add to this list?
If shorting is allowed , you should use the RF asset together with one of the Corner Portfolios that suit the RRTTLLU. Find the w and 1-w and solve for the E® and the E(SD).
If shorting is NOT allowed, and there is nothing specifically mentioned about maximizing returns for levels of risk taken, or maximizing the Sharpe or Roy’s ratios then just select two Corner Portfolios, find the w and 1-w and solve for the E® and the E(SD).
If shorting is NOT allowed, and there IS something specifically mentioned about maximizing returns for levels of risk taken, or maximizing the Sharpe or Roy’s ratios then we have to look at the individual returns, standard deviations, sharpe ratios and roys safety and use the Rf asset and ONE of the Corner Portfolios
^ It’s not correct. Example 10 shorting is not allowed still use CML method.
If the tangency portfolio exceeds the return requirement, you would combine it with the risk-free rate. It’s not borrowed.
Thus, apart from 3 scenarios mention by arigolden, another potential question may be, if shorting is not allowed, will the tangency portfolio be the optimal asset allocation for the client?
Kind of tag-along question here, from the paragraph immediately preceding example 10 (2015 curriculum, reading 18):
“On the other hand, as in Example 10, the highest-sharpe-ratio efficient portfolio’s expected return may be below the return objective. Assuming that margin is not allowed, in such cases the highest-Sharpe-ratio portfolio is not optimal for the investor.”
However, in example 10 the highest-sharpe-ratio corner portfolio _ IS _ greater than the return objective of 6.5%. Is this a typo???