Portfolio Optimization
Perhaps you want to set up your portfolio using the standard mean–variance optimization framework. That's still possible, but of course there are some things to consider when dealing with alternative assets.
Infrequency of pricing means that returns tend to be smoothed. Considering the effect on measured risk, how would you expect the allocation to alternative assets to be biased with mean–variance optimization?
Exactly!
No, alternative assets would be overallocated.
The smooth prices would make those asset classes look less risky for the returns offered, and it would appear like a better deal than it actually is. So investors sometimes add constraints to allocations with this approach.
Suppose you allowed for unconstrained optimization and told your computer you wanted the highest possible returns. How many asset classes would you estimate the computer would suggest?
Exactly!
Actually, it should suggest just one asset class.
If you tell the computer that private equity has the highest expected return of all asset classes and then ask the computer for the highest expected return for a portfolio, it will tell you to put 100% in private equity. No surprise there.
What would it suggest if you asked for minimized risk?
That's it. Again, not too helpful. So you're probably looking for something in between that considers both risk *and* return. By restricting the allocation ranges of certain assets, the efficient frontier is lower than the unconstrained frontier, but again, that includes some highly questionable risk measures anyway.
No, you can be safer than that.
Not really; think of *minimized* risk.
So you might decide to look at a different approach: mean–CVaR (conditional value at risk) optimization. How would you expect such an approach to view an asset for which returns are highly negatively skewed?
Probably not. If there's a large, negative skew, then this will tell you something about the value at risk for this asset class.
Absolutely. Looking at assets through a risk lens can allow for minimization of those left tail threats to the portfolio. This is more challenging, as it requires more historical data and simulations. But then the CVaR can be minimized subject to some minimum return constraint.
Not really. There's little opportunity (at least on the long side) from choosing an asset just because of a negatively skewed return distribution.
Perhaps you end up with one suggestion from a mean–variance optimization, and another from the mean–CVaR optimization, requiring a 5% minimum expected return:
| | Volatility | 95% VAR | 95% CVaR |
|-----|:-----:|:-----:|:-----:|
| Mean–Variance Optimal | 7.3% | -3.7% | -7.7% |
| Mean–CVaR Optimal | 7.8% | -4.1% | ? |
| Combination | 7.5% | -3.7% | ? |
Where do you expect those last two numbers to be, relative to the 95% CVaR shown?
No, they would be higher, or better:
Right!
| | Volatility | 95% VAR | 95% CVaR |
|-----|:-----:|:-----:|:-----:|
| Mean–Variance Optimal | 7.3% | -3.7% | -7.7% |
| Mean–CVaR Optimal | 7.8% | -4.1% | -6.8% |
| Combination | 7.5% | -3.7% | -7.3% |
The whole point of a mean–CVaR approach is to minimize that left-tail risk. So relative to the portfolio suggested by mean–variance optimization, the mean–CVaR portfolio will have a better-looking value at risk. And of course, a combined portfolio averaging these recommendations will land you somewhere in the middle.
To summarize:
[[summary]]
Overallocated
Underallocated
Other responses
1
Cash
Bonds
Diversification
The same as any other
As an opportunity to be exploited
As a threat to be minimized
Lower (further from zero)
Higher (closer to zero)
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