Alternative Asset Allocation Approaches
For any portfolio allocation, you want to know something about risk, return, and behavior in the total portfolio. With alternative assets, there are some statistical properties about returns to consider that lead to various approaches for asset allocation decisions.
For the second issue, consider return distributions themselves. Stock returns aren't normal; they have some skewness and excess kurtosis. How would you characterize alternative asset returns by comparison?
They aren't, actually.
That's right.
Recall the "fat tails" distributions of asset classes like hedge funds, to the point where survivorship bias is a real issue with any current listing. What statistical property measures fat tails?
First, consider the returns themselves; you don't always see continual or even daily prices for many alternative assets. How would you expect risk measures to be biased because of this?
No, they would be understated.
Absolutely.
A single quarterly valuation, such as a real estate appraisal, would severely understate risk by ignoring unseen price movements during the quarter.
So fine. You can always use that "square root of time" trick: $$ \sigma_{ann} = \sigma_t \sqrt{t} $$ to adjust standard deviation of returns, right? Well, no. This assumes uncorrelated returns. If stock returns bounce around up and down, unrelated to each other, there will be a certain volatility.
But now imagine that these returns are serially correlated. An up move suggests another up move, etc. How would this affect volatility?
No, it would be higher.
Exactly!
If several returns all go in the same directions, the ups and downs will be more pronounced, meaning greater risk. How can this relationship be summarized in terms of "smoothing," meaning lower measured volatility?
Not really. The smoothing comes from the irregular pricing itself.
Not quite. The smoothed volatility is low just due to the lack of regular pricing.
That's it! You can see this relationship in the stock and bond data here, using quarterly data from 1997 to 2017:
| Asset | Serial Correlation | Volatility reported | Volatility unsmoothed |
|-----|:-----:|:-----:|:-----:|
| US Equities | 0.03 | 17.0% | 17.7% |
| Emerging Market Equities | 0.17 | 26.2% | 30.8% |
| Government Issues | -0.01 | 4.9% | 4.9% |
| Broad Fixed Income | 0.02 | 3.4% | 3.5% |
| High-yield Credit | 0.34 | 10.0% | 14.3% |
| Inflation-linked Bonds | 0.12 | 5.0% | 5.7% |
Based on this, consider that the serial correlation for distressed securities hedge fund (HF) returns was 0.36, with reported volatility of 8.9%. What would be a fair estimate of unsmoothed volatility?
Somewhere around there is reasonable, yes! Take a look:
Not quite. Just as similar serial correlation for high-yield credit led to about a 40% difference (4.3 percentage points), the difference for distressed HF is about four percentage points as well. Take a look:
| Asset | Serial Correlation | Volatility reported | Volatility unsmoothed |
|-----|:-----:|:-----:|:-----:|
| Equity-market-neutral HF | 0.17 | 3.5% | 4.1% |
| Distressed HF | 0.36 | 8.9% | 13.0% |
| Commodities | 0.14 | 25.2% | 28.8% |
| Public Real Estate | 0.15 | 20.4% | 24.0% |
| Private Real Estate | 0.85 | 4.6% | 13.8% |
| Private Equity | 0.38 | 10.0% | 15.7% |
Unsurprisingly, this first statistical issue is most pronounced with those rarely priced categories of private real estate and private equity, both of which lean on appraisals and estimations.
No, that assumes normality.
Not quite; this is a measure of asymmetry.
Exactly! Recall that the normal distribution has kurtosis of 3, and a leptokurtic distribution with fat tails has a kurtosis measure of more than 3, or excess kurtosis more than 0.
If the left tail was fatter than the right tail (more extreme losses than gains), what would you see in terms of skewness?
That's not it. Skewness of 0 means symmetric, like the normal distribution.
No, positive skewness is seen for series like personal income, where the left side is bound and there are some very high outliers.
Precisely. And you'll notice both non-normality measures all over the alternative investment universe, especially when compared to US stocks and broad fixed income:
| Asset | Skewness | Excess kurtosis | Observed 95% VAR |
|-----|:-----:|:-----:|:-----:|
| US Equities | -0.51 | 0.43 | -17.7% |
| Broad Fixed Income | -0.05 | -0.41 | -2.4% |
| Equity-market-neutral HF | -1.17 | 3.55 | -3.9% |
| Distressed HF | -1.25 | 3.52 | -11.1% |
| Commodities | -0.71 | 1.62 | -30.6% |
| Public Real Estate | -0.88 | 4.60 | -24.5% |
| Private Real Estate | -2.80 | 9.62 | -15.4% |
| Private Equity | -0.46 | 2.05 | -15.7% |
These two important statistical issues lead to the following three main approaches to asset allocation for alternative assets. Which one would seem least appropriate for something like private real estate?
Not really; you can flexibly incorporate a lot of assumptions in a Monte Carlo simulation.
Right. At least before exploring each of these three further, a traditional mean–variance optimization seems the most limited in this space, given its reliance on variance, and the refusal of alternative asset classes to provide good variance measures.
So there are advanced methods for dealing with these fat tails and negative skews. There are time-varying models, regime-switching models, and extreme value theory, among others. Just be sure to unsmooth returns when necessary: or your portfolio may take you down a decidedly unsmooth path!
Not really. A risk-factor-based approach can be very instructive by using an integrated risk framework.
To summarize:
[[summary]]
Closer to normal
Even more non-normal
Overstated
Understated
It would be lower
It would be higher
More serial correlation means more smoothing
More serial correlation means smoothed volatility will be higher
More serial correlation means unsmoothed volatility will be higher
Other responses
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Standard deviation
Skewness
Excess kurtosis
Zero skewness
Positive skewness
Negative skewness
Mean–variance optimization
Monte Carlo simulation
A risk-factor-based approach
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