17.... I asked to 137 graduate students the following question: “For the following 10 years, do you prefer an investment with an annual return of 16% and a Sharpe ratio of 0,4 or another investment with an annual return of 13% and a Sharpe ratio of 1,3?” All of them (the 137 graduate students) preferred the first investment. And you?

I prefer the second, and his graduate students must not have thought about it much. But you do need to

*do* a calculation. I have to work it out slowly, using a calculator and a scrap of paper, but I'd expect a grad student in economics to do it in their heads--or, at least, to take the time to do it.

Apparently unlike Fernandez, I personally dislike volatility

*and I have a right to my preferences*. I'll get to "volatility versus risk" in a minute. I think I know my risk tolerance, and that tolerance creates a "risk budget" in my investing.

If we assume a riskless return of 3.5%, about the historic average for Treasury bills, then the first investment must have a standard deviation of 13%/0.4 = 32.5%, and the second must have a standard deviation of 10%/1.3 = 7.7%. The second has much lower volatility.

Well, a person who does no computations says, so what? It's all about the moolah, the bread, the spondulix, the Benjamins and rubs his thumb and index finger. Show me the money. I don't care about volatility so I won't even look at it or do any calculations with it.

Very well. Let's say

**I** can tolerate 7% volatility, and let's say that I use a balanced portfolio consisting Investment 2 and the riskless asset. In order to get the volatility down to 7%, I need to dilute it just a bit, 91% Investment2 + 9% riskless. That will dilute my return to 91% * 13% + 9% * 3.5% = 12.1%.

To get the volatility down to 7% with investment 1, I need to keep the allocation way down: 22% Investment1 + 78% riskless. That will give me a return of 22% * 16% + 78% * 3.5% = 6.25%.

In short, if I want the same volatility, using investment 2 will give me double the return. If I in fact am willing to tolerate the volatility of 100% Investment1, I still will get a higher return by leveraging Investment2. The cost of leverage complicates things, but with this big a different I think investment2 will still be superior.

If I use bonds instead of the riskless asset, I think the balance shifts even in further of Investment2.

Now, about risk and volatility. I agree that risk is complicated and multidimensional. But volatility is a form of risk, and e.g. Warren Buffett never said "volatility is not risk," he made a much more nuanced statement, "volatility is not the same thing as risk." We can also ask whether the standard deviation captures the idea of volatility (since many of us feel different about positive and negative skew). None of this matters unless you can define and exhibit an

*appropriate* measure of risk and show that it is

**not** closely correlated with standard deviation. I believe that in fact risk is risk and most forms of risk go more or less together and that the standard deviation is probably a good a measure of risk as sticking a thermometer in your mouth to measure core body temperature.

I did a casual explanation of this once, plotting a form of risk I care a lot about (maximum drawdown) against standard deviation in the real world, in a bunch of selected mutual funds representing different asset types and risk categories, and I'll show the result in a second. The point is it may well be true that small fluctuations during "normal" market conditions may not predict "crisis risk."

But when you look at any long-term data, standard deviation

**includes** the numbers from crashes and in fact they carry a lot of influence on the long-term averages.

So, here's the "inappropriate" measure, standard deviation, on the X axis, and a more appropriate measure, maximum drawdown on the Y axis. Complaining that standard deviation isn't a perfect measure of risk is a red herring. It's no more relevant than saying "book-to-market is not value," or "the Dow Jones Industrial Average is not the market" or "your drugstore thermometer doesn't measure body temperature." No, but they're reasonably good, and good enough to be useful.

Now, who knows, maybe Fernandez would go further and say "so what? Drawdowns are not risk, either." He does say "what most equity investors do not like is bankruptcy, default." But I am pretty sure you could show a strong relationship between large market drawdowns and bankruptcies and default.

Values from PortfolioVisualizer, using all data available in PV as of 1/2018. List of points plotted:

GLD (gold ETF)

PCRIX (commodities fund)

VTSMX (total stock)

DFSTX (small cap value fund)

ULPIX (2X daily-leveraged S&P 500 fund)

FNMIX (EM bond fund)

VEIEX (emerging markets)

VGTSX (global ex-US, international stocks)

FJPNX (Fidelity Japan fund)

VBMFX (Vanguard Total Bond)

VWEHX (junk bonds)

LMVTX (Legg Mason Value Trust, once-legendary active fund)

COIN (Bitcoin ETF) -- just kidding

"CASHX" (PortfolioVisualizer's "ticker symbol" for one-month Treasury bills)
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.