A trend following fund friend sent this along this morning…

**Investment A example:**

Average annual return: 9%

Standard deviation of return: 6%

Worst case drawdown of approximately: 12%

**Investment B example:**

Average annual return: 30%

Standard deviation of return: 20%

Worst case drawdown of approximately: 40%

His comment:

“Most people prefer the safety of a 9% return with a 6% fluctuation. However, both investment risk/return profiles are the same. They offer the same ratios between average annual return and risk. Standard deviation of return is 67% of the average annual and worst case drawdown is 33% larger than the average return. People’s natural biases tend to lead them into thinking lower returns means lower risk [but is that true?]. If you’re going to accept those risk ratios then why not shoot for the higher return in the process?”

Thanks.

Oh my goodness, this is so true. We are having the same issue at the moment. AND…not just amongst “people” but highly educated professionals in the investment and asset allocation business!

We now offer a ‘low vol’ product alongside our normal product that is simply 50% of the leverage. Same strategy, half the returns and draw downs. The ratios are exactly the same, yet the ‘low vol’ product is somehow more acceptable! Actually, when you add costs and fees, the ‘low vol’ product is slightly WORSE, yet more acceptable.

Again we find that top returns and top performance is penalized in this industry; mediocrity is celebrated and attracts all the assets. .

Mr Covel: Many of your observations are insightful and valuable, but this is a horrible example. Average returns can be misleading — but they are more misleading in a higher volatility portfolio. The compounded return (i.e. geometric average) is the relevant measure.

Here’s a dramatic example using a high volatility portfolio:

Year 1 = +130%

Year 2 = -70%

The average return is 30%, but the compounded rate of return is approximately NEGATIVE 16%. That is, an investor who put $1 million into this fund had $690,000 after two years … even though the fund had a 30% average return!

Arguably, the return/standard deviation ratio needs to rise with higher standard deviations or you may suffer gambler’s ruin. That is, after a 90% drawdown, it is nearly impossible to recover. If you just keep increasing the return/standard deviation/drawdown ratios linearly, you will almost certainly suffer gambler’s ruin.

Perhaps you meant to write “compounded return” in your example, in which case the above paragraph is still true, however, your example becomes more meaningful.

@R Humberton

You do bring up a good point about “average returns”. However, trendfollowers do use CAGR/RoR (unlike mutual funds), but may refer to it as “average returns” for the lay person. The point of the example is if risk/return ratio is the same, why not shoot for the highest return? Makes total sense. To Etienne’s point, maybe this shows how our society thinks medocrity = winning. How sad!

Mr. Humberton is exactly right. Further, a client that sees a 40% drawdown can easily envision a 50% or 60% (or worse) reversal. Your model might say 40% is a “worst case” number, but the actual worst case can only be known in hindsight.

Mediocrity attracts assets because the investment industry has a long and rich history of blowing people up – not a single one of Etienne’s clients will be as familiar or as confident in his model as he is. They will naturally be skeptical, the “highly educated professionals” even more so (it’s a survival tactic). This skepticism and the corresponding regulatory burden that we bear did not rise out of a vacuum. Part of the price of managing other people’s money is paying for all the sins of those that came before you.

You make a very good point, Strom.

Even if we can ensure (due to the statistical confines of a mechanical system), the perception as you point out will always be there.

No, Humberton is wrong. Everybody knows that average annual return is not calculated by adding up the return each year and then dividing by the number of years. It is calculated by calculating the nth inverse root (where n is number of years) of the total compounded return.

I also think that mediocrity attracts assets because most people want to be mediocre, not becuase of blowups. That is in fact the real survival tactic. Its because people haven’t yet adapted to a culture of abundance. They are still stuck in the caveman days when it didnt make sense to kill more than you could eat.

Mr Humberton, I know what you mean, but I bet that Mr Covel or the fund friend that he quoted was talking CAGR, whenever I hear “average returns” even in the hedge fund or mutual fund industry of course we all think of compounded.

I think it’s pretty absurd talking in arithmetic averages in an environment that is exponential that requires therefore geometric averages.

It would be absurd to say that Warren Buffet for the last 40 years has made an average of 10,000% a year (arithmetic) when compounded this is around 20’ish % yearly.

Let’s assume that this is compounded return, still:

my point is a simple one. In Mr. Covel’s example, if ALL I knew about the fund was the information he presents, and I was forced to invest in either fund #1 or fund #2, I would choose fund #1. The reason is a simple one, and it has nothing to do with mediocrity. Rather, it looks like the two funds may be doing the same thing, and the only difference is fund #2 is running with 3.33x the leverage of fund #1. Adding leverage does not add value! But it adds the risk of gambler’s ruin. And there is simply not enough information provided to assure an investor that there is no risk of gambler’s ruin!

For example, let’s assume there is a fund #3, and it’s running at 2.5x the leverage of fund number #2 … does that make it superior to both fund #1 and fund #2 even though it has a 99% drawdown (but higher average returns of ciyrse?) At what point does one say that this fund manager is simply gambling with other people’s money?

How can one tell???

RHumberton (and everyone else)… you’re making this harder than it has to be.

First, we all know (at least I hope we do) that you can’t just take percentages and add/subtract/multiply/divide them. The examples cited here OCCUR AT THE SAME TIME, NOT DURING DIFFERENT TIME PERIODS. Therefore they CAN be compared to each other without having to do any math, as the monetary value of the account at the start doesn’t change. It doesn’t matter whether you’re compounding anything or not as long as you’re treating both scenarios equally.

Second, drawdown is a direct effect of risk. You don’t need to know what the leverage is… a 40% drawdown of account value is a 40% drawdown, and a 12% drawdown is a 12% drawdown. It’s a constant in the examples… it doesn’t change if the leverage changes. The only thing that changes if the leverage changes is the drawdown percentage itself… becoming a larger drawdown with a larger position size/leverage and smaller with a smaller position size/leverage. Stop trying to make it seem like you need to know anything else… all of the information you need is there. The risk of ruin doesn’t change… just like the performance sigma of standard deviation wouldn’t change. The only way you would reach ruin is to increase the position size/leverage to a point that the drawdown reaches 100%.

I think most of the people arguing these points would do well to study up on money management so that you understand what is actually being said.

Trader Jim:

It’s often a sign of intellectual weakeness when someone starts insulting other posters, as you did in your last sentence. I don’t know anything about you, and I will give your comments the respect they deserve (more on that below), however, it’s both foolish and rude to assume that others know less than you.

On the substance, you are simply wrong. If you run two funds (Fund #1 and Fund #2), and they pursue identical strategies — with the sole difference that your back office runs Fund #2 with 3.33x leverage — the results will be what Mr. Covel illustrated. [Unless I made an arithmetic mistake 😉 ]

Furthermore, since I presume that you charge an incentive fee on gains, you are motivated to run your funds with the maximum leverage possible, because heads you win — tails your investor loses. There is NO alpha associated with leverage. The alpha comes from an improving Sharp or Sortino or other ratio. And in Mr. Covel’s example, there is no improved ratio. Just move leverage.

On the subject of Gambler’s Ruin, you are wrong again. A portfolio manager doesn’t have to literally lose 100% to experience Gambler’s Ruin. The reality, is that if you lose much more than 50%, you will either be fired by your boss, by your investors, or by your margin clerk. And that’s ruin, unless you are one of the many unsavory CTA’s, who after blowing up their clients, just closes the old fund, starts a new fund and blows up a new group of investors.

The bottom line is, I believe that Mr. Covel was trying to make a salient point (regarding so-called Prospect Theory in the Behavioral Finance literature) — however, his illustration not only didn’t demonstrate Prospect Theory, but rather it demonstrated the opposite.

Perhaps Mr. Covel will comment on this thread and adjust his illustration, so we can see if my interpretation of his intent is correct. If he wants to tweak the numbers to better illustrate his point, I for one will not hold that against him!