# Corner portfolios and optimal asset allocation

Hi all I am revising the asset allocation part, and i am a bit puzzled with two examples 9 & 10, page 216 volume 3. Example 9 shows that the optimal portfolio for the client lies between two corners portfolio, thus to establish the right asset allocation it calculates the percentages that equal the expected return of the two portfolios to the required return. Example 10, similar problem, instead takes the first corner portfolio with higher expected return and it consider it the best asset allocation. why is that? why didnt they took a portoflio lying on the MVF between two corner portfolios as in previous example? many thanks

Because the corner portfolio they picked had the highest SR. SO moving away from this along the MVF would just lower SR.

I don’t have it in front of me but I’m guessing that in scenario 2, there are no short sale constarints (ir you can borrow at the risk free rate). If you can borrow at the risk free rate then you choose the corner portfolio that meets your return requirement and has the highest Sharpe Ratio. You calculate your weights the same way as in scenario 1, but you’ll find you have a negative weight in the risk free rate and more than 100% in the ideal corner portfolio.

Glad you pointed these out…I might have skipped over them otherwise. The distinction in more complicated than I had assumed when I read (okay, skimmed) these examples first time through. Seems that in Example 9, in order to get a higher Sharpe Ratio, you’d actually have to lower the return of the portfolio below the minimum acceptable return. So, the combination of portfolios 3 and 4 is the best you can do from a risk-adjusted return perspective (with no borrowing) while still meeting the return goal. In Example 10, however, the tangency portfolio (which has the highest Sharpe ratio) satisfies both the return objective and the risk tolerance. Although we could combine that portfolio (number 4) with portfolio 5 a lower Sharpe Ratio would result. Same is true (as is shown in the example) if you combine the tangency portfolio with the risk-free security to satisfy the 6.5% return requirement with the lowest std dev. The deciding factor among all the choices seems to be that the client specifically wants to minimize shortfall risk below the spending rate. The tangency portfolio has the lowest shortfall risk (highest Safety-First Ratio) among the options, so that’s the correct choice. Aside from all the details, I guess the big take-away is that the answer to these corner portfolio questions isn’t always just the weighted average of the two nearest corner portfolios… Oh well…

^Both approach are acceptable! On the exam, just pay attention to the question, it will ask you which way you should use. Read the short-sale rule too, it will give you clue also.

If there are short sales, there are no corner portfolios… If there is no constraint against leverage/borrwoing then take the Tangency Portolio and borrow or lend If there is a constraint take the two corner portfolios that the return objective falls between.