Turtle Trading Rules

Chapter 14 How to Measure Risk (2)
For a particular trading system, return refers to your expected return from using the system.We can quantify returns in many ways, here are a few that I find useful:
Geometric average return: The average compound growth rate, also known as the geometric average rate of return, refers to the average compound interest rate within a specific investment period.The rolling growth of assets at the beginning of the period at this compound rate will just grow to the level of assets at the end of the period.For simple interest-bearing accounts, the average compound growth rate is the interest rate (compound interest) itself.As long as there is a particularly high rate of return in a given period, the overall average compound growth rate indicator will be significantly affected.

Average one year trailing return (average one year trailing return): This refers to the one-year average return calculated on a continuous rolling basis.This metric better reflects the typical level of returns in any given one-year period.For tests spanning more than a few years, the indicator is relatively insensitive to a period of particularly high returns.

Average monthly return: This refers to the average return of each month during the test period.

In addition to these numerical indicators, I also found several useful tools.One is the equity curve itself, and the other is like a chart that highlights the distribution of monthly returns.I also like to examine monthly returns over a period of time.This graph shows the monthly returns of the Donchian Trend System from January 1996 to June 1.

1996年1月~2006年6月我发现，像图7–5这样的图能很好地反映风险与收益的权衡，比单纯的一个或一组数据要生动得多。

A composite measure of risk and return
To compare different trading systems or fund managers using trading systems, there are several common composite metrics available.The two most commonly used indicators are the Sharpe ratio and the MAR ratio.

Sharpe ratio
The Sharpe ratio is probably the most common metric used by retirement funds and large investors when comparing potential investment targets.The Sharpe ratio was invented by Nobel laureate William F. Sharpe in 1966 to compare the performance of mutual funds.Originally known as the Return-Volatility Ratio, this metric was later named after its founder and simply known as the Sharpe Ratio.

The Sharpe ratio is derived by first calculating the excess rate of return (that is, the average monthly or annual compound growth rate during the period minus the so-called risk-free rate of return, or minus the risk-free rate such as short-term treasury bonds). interest rate on a bond) and divide it by the standard deviation of the period's return (typically monthly or annual return).Remember that the Sharpe ratio was invented for comparing the performance of mutual funds, not as a general measure of risk-reward ratio.A mutual fund is a very specific investment vehicle that primarily makes unleveraged investments in a portfolio of stocks.

The Sharpe ratio is used to compare mutual funds, and this raw positioning also provides important hints about risks that are not covered by it.The Sharpe ratio was proposed in 1966, when mutual funds only made unleveraged investments in U.S. stock portfolios.Therefore, comparing mutual funds compares investments in the same market, but with essentially the same investment strategy.

In addition, mutual funds at the time generally engaged in long-term investment in stock portfolios.Since there are no factors of timing and trading methods, the difference between different funds is only the difference in portfolio selection and diversification strategy.Therefore, the Sharpe ratio is a good proxy for the level of risk when measuring mutual fund performance because it correctly reflects the fact that the level of risk is directly related to the volatility of returns for comparisons over the same period.All else being equal, a mutual fund with low volatility is less likely to deviate from its historical average return.

But while the Sharpe ratio is an excellent risk-reward metric for comparing equity portfolio management strategies, it is not a good enough comparison metric for alternative investment funds such as futures hedge funds.I say this because these alternative investment funds differ from an unlevered stock portfolio on several important levels of risk:

Risk management strategies: Futures systems and futures funds often use short-term trading strategies, which are very different from the long-term holding strategies of traditional investment funds.Losses can occur much faster when using this trading strategy that requires frequent buying and selling.

Diversification strategy risk: Many futures funds and trading systems are not inherently diversified to the level of traditional investment funds, often concentrating a substantial portion of assets in a small number of instruments.

Potential risks: The leverage level of futures trading is higher than that of stocks, which invisibly makes futures traders bear greater risk of market fluctuations.

Confidence risk: Many futures fund managers do not have a detailed history.In the absence of references, the investor's risk of not getting the expected return will increase.

Sadly, the popularity of the Sharpe ratio seems to exacerbate a problem I see in this industry: the stability of returns as the only measure of risk levels.This problem is especially acute for those who do not understand trading and how trading strategies differ from holding strategies in traditional stock investing.

I must emphasize one point: Stability does not mean low risk, and very high-risk investments may also generate stable returns over a limited period of time.It's easy for investors to believe that an investment or investment manager that consistently delivers positive returns over a period of several years is a safe bet.They just harbor this belief blindly, often without knowing how the rewards are earned.

I believe that in many cases, the greater the stability of returns, the greater the actual level of risk.I can give two examples: one is LTCM, which used a strategy that was quite successful for the first few years, but then completely failed and created a disaster; the other is a strategy that many funds still use today, It performs very well, but there is also the risk of a momentary crash.

LTCM's strategy is based on two bases: one is very high leverage, and the other is the uniform tendency of the prices of fixed income bonds under certain circumstances.Its extremely high leverage makes its positions exceptionally large, so when it suffers a loss, it is very difficult to get out of it.

The strategy worked well for a few years, but LTCM's size hurt it when the financial crisis created by the Russian bond default triggered an unfavorable volatility.Because the other camps in the market know that they can let the price continue to move against LTCM, and in the end, LTCM will be forced to reverse their positions sooner or later.In the end, LTCM nearly wiped out its fortunes, which were worth $47 billion before its collapse.

Before the crisis, LTCM had average annual returns of almost 40%, and it was pretty consistent.In other words, its Sharpe ratio is outstanding.You can read more details about the story of LTCM's downfall in Roger Lowenstein's book When Genius Failed.

Hedge fund Amaranth had a similar problem recently with its natural gas trades.Like LTCM, Amaranth's position was too large for other traders. Amaranth lost 90% of its $65 billion in just two months.Before that, it also had a decent Sharpe ratio.

Today, there are many hedge funds that make money by trading currency options, which means they are betting on drastic changes in prices.If the risk is managed effectively, this can be a very effective strategy that provides very consistent returns.

The problem is, the actual risks these funds face are hard for laymen to understand.They can generate strong and stable returns while being heavily exposed to price volatility of all kinds.For example, any seller of 1987 Eurodollar options could go bankrupt.Losses from price volatility, combined with the risk of option exercise, can easily cause losses in one day to exceed the value of the entire fund.

Prudent fund managers limit these risks.Unfortunately, many investors are unaware, and by the time they realize these risks are often too late, they have already lost everything.They are lured by the fund's stable rate of return and good performance over the years, but they don't know that these funds have not experienced real tough times.

MAR ratio
The MAR ratio is a metric created by Managed Accounts Reports, Inc., a company that specializes in reporting the performance of hedge funds. The MAR ratio equals the average annual return divided by the maximum drawdown, which is calculated from month-end data.This ratio is a fairly quick and straightforward measure of the risk-reward ratio, and I've found it to be very effective in weeding out underperforming strategies.It's an excellent tool for rough analysis.Taking Donchian Trend System as an example, during the test period from January 1996 to June 1 mentioned above, the MAR ratio of the system was 2006, among which, the average compound return rate was 6%, and the maximum calculated using the end-of-month data was 1.22. The decline rate is 27.38%.

I find it somewhat unwarranted to use end-of-month data to calculate the magnitude of the decline, as it often underestimates the actual magnitude of the decline.So I'm using a peak-to-trough drop in my own tests, without regard to what day of the month those highs and lows are.To see how this approach differs from using month-end data alone, just look at my calculations: the actual decline including non-month-end days is not 22.35%, but 27.58%, so the actual MAR ratio is 0.99, while Not just 1.22.

Imitation Effect and Risk of Systemic Mortality

When it comes to trading systems, strategies, and performance, one of the most interesting phenomena I've observed is the imitation effect: Strategies with an impressive track record in risk-reward ratios tend to be the ones most easily imitated by the industry.They are just emerging and immediately followed by billions of dollars, only to destroy the Great Wall because they have grown beyond the capacity of the market.In the end, they fell prey to the death of the system early on.

Arbitrage strategies are probably the best example of this at this point.Arbitrage in its purest form is actually a risk-free trade.You buy something in one place, sell it for a premium in another place, deduct shipping or storage costs, and the rest is your profit.Most arbitrage strategies are not completely risk-free, but many come close.The problem is that there is a prerequisite for making money with such a strategy, that is, there is a price difference between the same instrument in different places, or there is a price difference between one instrument and another similar instrument.

The more people who use a particular strategy, the faster the price difference disappears because these traders are essentially all competing for the same opportunity.Over time, this effect can ruin the strategy as it becomes increasingly unprofitable.

On the contrary, systems and strategies that are not attractive to ordinary investors have a longer life cycle.Trend following is a good example.Most big investors have a hard time with the big drawdowns and swings in value that are so common to trend-following strategies.Because of this, trend-following strategies consistently work over the long-term.

However, the return levels of trend-following strategies are cyclical.Whenever a large amount of money follows the trend after a period of relatively stable returns, there are usually a few relatively difficult years because there are too many investors using the same strategy in the same market, and the market cannot easily absorb so much funds.Conversely, when investors withdraw their money after a relatively tough period, good times usually follow.

Don't expect too much: If you are too greedy when testing a strategy, you are more likely to not get the results you want.Strategies that have historically appeared to be superior are also the most likely to attract new followers, and when newcomers join in, they often cease to be miraculous very quickly.

Each of us has different risk tolerance and return expectations.Therefore, there is no one-size-fits-all indicator that is attractive to everyone in the world.I have used a combination of MAR ratios, declines, and overall returns to judge return stability by looking at Sharpe ratios and R-squared values.Recently, I have designed some new indicators, which can be said to be more stable versions of these commonly used indicators.I will introduce these indicators.

I will also try my best not to be confused by some special data, because I know that the future is not equal to the present, and a strategy with a MAR ratio of 1.5 now does not mean that it can maintain this level in the future.

[6] LTCM is a hedge fund mainly engaged in arbitrage activities of fixed-rate debt instruments. Founded in 1994, it is mainly active in the international bond and foreign exchange markets and specializes in financial market speculation. It is called together with Quantum Fund, Tiger Fund and Omega Fund. The four major international "hedge funds".Its performance was once brilliant and attractive, but in the global financial turmoil in 1998, it came to the brink of bankruptcy. In the end, the Federal Reserve came forward to organize and arrange for 15 international financial institutions led by Merrill Lynch and Morgan to inject capital and jointly take over the company, thus avoiding its bankruptcy. ——Editor's note
(End of this chapter)