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Performance and Risk


Here's where a typical trading subscription site shows you charts and tables of past performance to convince you that their trading system will make you rich. Because we offer a backtester app, we don't need to: head on over to the Backtester App and see for yourself.

Plus, you can use your own custom portolio. Since we're not mind readers, we can't generate these charts prior to your visit.

Instead, one can verify whether the backtester is accurate. For each period (e.g. each month) in the backtest, we display the trade date and the ranking order of funds used to determine the fund(s) to be invested for the next period. For example, if the backtester setting "Trade Delay" was set for 1 day, then use the Scoring App to verify the ranking order of funds 1 day prior to the trading date. (Trade date of May 31, 2013 would mean using the scores from May 30, 2013.) Then use Yahoo! Finance historical prices to determine whether the % gain for the next period is accurate. Note that the backtester app mimics how mutual funds are traded: at the end of the trading day, after close, the funds are swapped before the start of the following trading day. Also, no commissions, slippage or taxes are used, to mimic how 401k accounts typically operate.

Why It Works

Price Momentum

401kBooster.com uses deploys the Asset Class Rotation Investment System (ACRIS) which is essentially a trend-following strategy that searches for the fund with the greatest positive price momentum of intermediate length (1 to 12 months). In order to score well, the security needs to demonstrate a trend.

The evidence for a “momentum effect” in equities is large. Many studies report positive abnormal returns if equities are bought based on past three to twelve month returns and then held for one to twelve months. Long positions are created for the fraction of equities demonstrating the highest recent returns, and/or short positions are created for the fraction of equities demonstrating the lowest recent returns. All of these combinations generate returns greater than a matching baseline index. A recent study “A Century of Evidence on Trend-Following Investing” by AQR Capital Management examined a century of market returns based on a simple trend following metric and found consistently good performance across multiple markets.

Trends or “momentum effect” are usually believed to be the result of cognitive biases in investors. Many experts agree on this point. What is less well understood is the specific bias that causes momentum. Some believe that momentum comes from an over-reaction to information or to simple increase in price. Others believe that momentum comes from an under-reaction to earning news and other information. See Wikipedia article on price momentum. ACRIS relies on the momentum effect to continue to be present in the future. The markets are a human construct, and as long as people continue to trade, we believe price momentum will continue to exist.

End-of-month Bias

In examining the historic stock returns in the US, many have noticed a distinct pattern where the end and beginning of the month tend to have higher price movements (on average). The effect is strong enough for some to create a trading system based on this end-of-month bias. Since the day of the month to evaluate and trade the asset portfolio, ACRIS chooses to try to take advantage of this by trading on the last day of the month.

Most hypotheses to explain the end-of-month bias revolve around the cognitive bias to end financial periods with the change in month. These include pay check deposits, 401K contribution payouts, institutional fund performances tied to end of months, etc.

Not by Market Timing

A common misconception is that in order to trade effectively, we need to time the market: buy at the trough and sell at the crest. The implication is that one needs to predict future direction of the market. It doesn't take the myriad of studies to confirm what most people instinctively understand: the market is random and so predicting the exact future is a fool's game.

Instead we are following trends. We buy after the trend is already going up, and we sell after the upward trend appears to be slowing down and another security exhibits a stronger upward trend. The scoring calculation is not a prediction of the future, but rather a determination of the strength of the security's upward trend. We rely on the momentum effect to provide us with the statistical edge.

Risk

Volatility and Drawdowns

Two standard metrics of risk are volatility and drawdown. Volatility is usually measured by the variance (or standard deviation) of returns (daily, monthly, annually). Drawdowns are the percentage loss from the last equity high.

Volatility has the problem that large gains and small losses at equal frequencies have the same volatility as small gains and large losses at equal frequencies. Hence, volatility does not capture well the human view of risk where large gains and small losses are not considered risky.

Maximum drawdown is a more intuitive measurement of risk because people feel loss relative to their equity's highest value reached. However maximum drawdown does not inform on the length, frequency, and average size of drawdowns that may affect a person's sense of risk.

The ulcer index attempts to capture with a single value, the length, frequency, and size of drawdowns throughout the backtest period. Similar to the formula for standard deviation, the ulcer index is the square root of average sum of squares of the instantaneous drawdown percentage. (Standard deviation of returns is roughly the square root of average sum of squares of the difference between return and average return.) The smaller the ulcer index, the smaller the length, frequency, and/or size of drawdowns.

401k Booster Performance from Backtester App, Recommended Trading Strategy, 1/1/1995 to 1/1/2015
Equity $ Gain from $10K CAR % GSD % Max DD % Ulcer Index
Standard Portfolio $1,369,669 27.9 21.6 -25.9 7.3
Basic Portfolio $501,833 21.6 16.9 -28.0 8.5
TSP Portfolio $245,232 17.3 15.8 -19.5 5.5
S&P 500 (VFINX) $64,044 9.7 21.4 -55.3 17.9
US Aggregate Bond Index (VBMFX) $32,160 6.0 4.5 -5.5 1.4

To compare performance among systems with different risk, we can use adjust the returns by a risk metric. The Sharpe Ratio is a risk adjusted performance measured defined by: (CAGR - risk free rate) / Standard Deviation. The risk free rate is the rate of return an investor can receive at zero risk. Traditionally one can use 3 month US Treasury Bills as a proxy, which historically have averaged a 4.6% annual rate of return, though for the past 20 years, the average annual rate has been 2.6%. The Martin Ratio is (CAR - risk free rate) / Ulcer Index. The MAR Ratio is (CAR - risk free rate) / Maximum Drawdown.

401k Booster Risk Adjusted performance with risk free rate = 2.6%, Recommended Trading Strategy, 1/1/1995 to 1/1/2015
Equity Sharpe Ratio Martin Ratio MAR Ratio
Standard Portfolio 1.17 3.45 0.97
Basic Portfolio 1.12 2.17 0.66
TSP Portfolio 0.93 2.67 0.75
S&P 500 (VFINX) 0.33 0.40 0.13
US Aggregate Bond Index (VBMFX) 0.76 2.43 0.62

Diversification

The most common advice to investors is to diversify to reduce risk while maintaining good returns. Avoid putting all the eggs in one basket. Yet our recommended strategy holds one position at any one time. At first glance this seems inordinately risky.

The purpose of diversification is to reduce risk. As described earlier, there are a number of ways to measure risk, such as: volatility (variance), drawdowns, and the ulcer index.

Diversification attempts to minimize large losses to equity by spreading the portfolio to different asset classes or investment instruments. Ideally, each component is uncorrelated, allowing individual components to be more volatile. The difficulty is that most investment instruments are substantially correlated. And during severe bear markets, relatively uncorrelated instruments often become significantly correlated (e.g. they all lose value) just when we need them to be uncorrelated.

The key insight is that diversification is only one of many tools to manage and reduce risk. There are other methods to manage risk. Diversifying for the sake of diversifying can lead to reduced performance without sufficient reduction in risk to justify reduced performance.

The recommended strategy manages risk in two ways. First, it already employs diversification in the form of using only a portfolio of funds that represent sufficiently sized markets. Each fund holds a diverse group of equities, so they provide sufficient diversification themselves to smooth out the volatility and enable the strategy to rotate funds on a monthly basis. Second, the strategy uses active management (monthly fund rotation) to limit time exposure of any fund that exhibit a downtrend.

Psychology

One of the biggest (if not the biggest) source of underperformance is the investor. Fear and Greed are powerful emotions that can cause the investor to stray from their trading strategy.

Fear, for example, can lead to behaviors such as leaving the market after losses and making those losses "permanent" by missing out on subsequent gains. Or fear regretting a loss, and therefore avoid selling a position to make the loss official, hoping that the position would recover. Greed can lead to refusing to exit a position because the security has been doing well and hoping that it will continue to do well.

The best course of action is to have a clear set of trading rules (what to buy, how much to buy, when to buy, and most importantly: when to sell) and then stick to them. Easier said than done. Learn discipline and learn about yourself. And fit the investment strategy to your temperment. Use the backtester app to gain confidence in the system. Paper trade (or trade with a relatively small stake) for a lengthy period of time to get a feel for the system and the variance.

Curve Fitting

The most important thing to watch out for while backtesting your system is curve fitting the inputs and settings of your system to optimize the results from the past. In particular with ACRIS, avoid choosing securities in your portfolio solely based on results from your backtest. The risk is ending up relying solely on luck for future results because by chance the backtest settings combined with your choice of securities in your portfolio had good historic performance. The choice of securities in the portfolio should have an underlying logical rationale, such as all recognized US industry sectors, commodities represented in exchanges, or other range of asset classes.

Good investing (and trading) is not relying solely on good luck; rather it is relying on having an "edge". Don't be the gambler in the casino, be the casino. Be careful not to delude oneself in finding this "edge" and having turn out to be solely a result of temporary good fortune in the backtest, not to be repeated in the future. When constructing your own portfolio, understanding variance (especially drawdowns) is also important as unexpected downturns can result in emotions that lead to underperformance. It is better to rely on general human behavior that repeats time after time for this trading edge than to rely on historical happenstance.

A quick example of curve fitting: Removing the Developed Asia Pacific Index (VPACX) from the Standard Portfolio would noticeably improve backtest results (go ahead and see for yourself.) However we keep this index in the portfolio because the portfolio was constructed to represent major capital markets by geography. Excluding Japan, the 3rd largest economy in the world, and Australia, the 12th largest, is violating the underyling rationale of the portfolio. Backtesting without the Asia Pacific Index may provide an overestimation of likely performance in the future.

System Death

System death is when an investment system that was previously profitable becomes unprofitable due to market dynamics. One cause is if a strategy becomes too popular and outgrows the liquidity of the market. For example, arbitrage strategies (where one purchases securities in one market and immediately sells in another market and pockets the price difference) become less and less profitable as more traders implement similar arbitrage strategies and the spread of prices between markets drop as they compete for the same trades.

Systems that don't appeal to the typical investor will have longer lifetimes. For example trend following tend to have significant equity fluctuations that many investors are uncomfortable with, so trend following works for longer periods of time. Many systems tend to be cyclical. Some strategies fall in and out of favor as capital follow recently well performing strategies. Mean reversion strategies ("buying the dip") are usually cyclical: years of good performance followed by years of poor performance and so on.

Systems that rely on natural human behavior has been working for a long period of time. Because ACRIS relies on price momentum, a phenomena that appears to have existed ever since markets have existed, we believe it will continue to perform well. However if the markets ever become dominated by mechanical (algorithmic) trading strategies, then price momentum and other phenomena based on human behavior may diminish, and a system like ACRIS may no longer perform as well.