# General performance of The Alpha Momentum Strategy relative to Buy & Hold:

$100k invested in the S&P 500 at the beginning of 1995 would have turned into roughly $900k by the end of 2017, including reinvested dividends. This equates to a compound annual return (CAGR) of roughly 10.8%. Not bad.

Despite that fact, an investor would have needed to endure multiple harrowing drawdowns, or periods of loss over that time period. The aftermath of the dot-com bubble and the great financial crisis (GFC) are the most obvious examples - the S&P 500 was at one point down almost 51% from its pre-GFC levels. This means that an investor who bought at the top had lost almost 51% of his money if he were still holding. The below chart shows the drawdowns a Buy & Hold investor would have needed to endure to enjoy the 10.8% CAGR over this time period.

# The Alpha Momentum Strategy is a superior option relative to Buy & Hold.

The below chart shows the comparison of an investment in the Alpha Momentum Strategy relative to an investment in the S&P 500 (including dividends) over the same time period. The Alpha Momentum Strategy shows a CAGR of 22.4% over this time period - more than double the 10.0% return of the S&P 500.

That's great, but returns are only one side of the equation when investing - what about the risks? If we talked about the drawdowns of Buy & Hold, we need to talk about the drawdowns for the Alpha Momentum Strategy as well. The Alpha Momentum Strategy exhibited a maximum drawdown (MDD) of -22.8% over this same time period, less than half the drawdown of the S&P 500's, which was -50.8%. Here is a chart showing the drawdowns of Buy & Hold relative to the Alpha Momentum Strategy:

This data shows that, not only did the Alpha Momentum Strategy outperform in terms of returns, but in terms of risk taken for those returns as well - an investor using the Alpha Momentum Strategy would have seen a much smaller drawdowns than an investor employing a traditional Buy & Hold approach.

# A deeper dive:

When choosing a system to trade, professional systematic investors look at a lot more than simply the annualized historical returns and worst drawdowns. Professionals look at things like volatility, downside volatility, numbers of periods with negative returns, the number and length of drawdowns below a certain threshold, and ratios that put these numbers in perspective. Here we will go deeper into the data to explore how The Alpha Momentum Strategy performs relative to Buy & Hold in terms of these often overlooked, but very important points of comparison. Here we will show that the Alpha Momentum Strategy has historically outperformed traditional Buy & Hold investing (as measured by buying and holding the S&P 500 - including reinvesting dividends) on all metrics.

Up until this point, we have examined **daily return streams**. For this portion of the discussion, we will examine **monthly return streams**.

### Compound Annual Growth Rate (CAGR):

This is obviously the first return metric investors reference. The Alpha Momentum Strategy has historically annualized more than double the return of the S&P 500. What is even more impressive is that the Alpha Momentum Strategy's calculation does not include the receipt and reinvestment of dividends, while the S&P 500 return stream does. This means that the real life execution of the Alpha Momentum Strategy over this time period would have likely outperformed the S&P 500 by even more. **Advantage - Alpha Momentum.**

### Maximum Drawdown (MDD):

Peak to trough, this is the most an investor would have lost had he been invested in the strategy during the test period at any given time. An investor in any strategy is either at an all-time equity high or in a drawdown.

Buy & Hold investing has historically induced extreme drawdowns. An investor in the S&P 500 had lost more than half of their invested capital during the Great Financial Crisis (GFC). Because of the risk mitigation strategies built into the Alpha Momentum Strategy, an investor in this strategy would have only lost about 17.3% of their invested capital during the worst time period for the strategy. **Advantage - Alpha Momentum.**

### CALMAR Ratio:

A common risk metric employed by systematic traders in evaluating systems is the CALMAR ratio, which is the CAGR divided by the inverse of the maximum drawdown [in formula: CAGR / -MDD]; typically, the higher the CALMAR ratio, the better, as an investor in a higher CALMAR ratio strategy is being better compensated for the risk they take relative to an investor is a lower CALMAR ratio strategy. Over this time period, the CALMAR for the S&P 500, including dividends, was about 0.2. The CALMAR for The Alpha Momentum Strategy was about 1.3 - about 6.5x higher than that of the S&P 500. This means that an investor in the Alpha Momentum Strategy not only significantly outperformed an investor in the S&P 500, but they did so with much less pain - the ride was smoother, meaning they were less stressed and more likely to stick with their stated investment objectives. **Advantage - Alpha Momentum.**

### Standard Deviation of Monthly Returns:

This is the simple statistical calculation of standard deviation as applied to the monthly return stream and expressed in annualized form. Put simply, the higher the number, the more volatile a strategy. That said, while standard deviation is a common risk metric used by the professional investment community, it fails to recognize the difference between "good volatility" and "bad volatility." If a strategy is producing strong positive results, this will impact the standard deviation in the same way as if a strategy is producing strong negative results; in reality, we want a strategy that has strong "upside volatility" and low "downside volatility." As such, we need a better measure to assess volatility in a strategy. So while the S&P 500 was less volatile as measured by standard deviation over this time frame, we will see later in this discussion when we discuss the Sortino Ratio and Downside Deviation that this wasn't necessarily a bad thing.

### Sharpe Ratio:

This is the annualized return (CAGR) minus the risk free rate (in this example, I set the risk free rate at 0) divided by the standard deviation. Higher numbers are better, because they indicate that an investor is being better compensated for risk taken. The S&P 500 generated a Sharpe Ratio of 0.69 over the test period while the Alpha Momentum Strategy generated a Sharpe Ratio of 1.48, more than 2x higher. **Advantage - Alpha Momentum.**

**Downside deviation of monthly returns:**

We said earlier that standard deviation didn't do the best job at explaining volatility because it penalized upside or "good" volatility just as much as it penalized downside volatility or "bad" volatility. This calculation adjusts for that and only considers downside or "bad" volatility. Downside deviation is the annualized calculation of the standard deviation of monthly returns that fall below a minimum threshold. Since I want to analyze months in which the system lost money, my "threshold" is 0 - therefore, this number looks at how bad losing months are for the system relative to the S&P 500. It is important to (a) realize that this number is an annualized calculation of downside deviation and (b) does not take into account the number of losing months over the test period (which will be addressed later). Over the test period, the annualized downside standard deviation of the S&P 500 was 16.8%, while the same measure for the Alpha Momentum Strategy was 12%. **Advantage - Alpha Momentum.**

### Number of months with a negative return:

Not only were losing months with the Alpha Momentum System not as bad as losing months with the S&P 500, but the S&P 500 had more losing months (92) than the Alpha Momentum System had (80). The Alpha Momentum System lost less often and lost less when it did lose than the S&P 500. **Advantage - Alpha Momentum.**

### Sortino Ratio:

I've heard this called the "Super-Sharpe Ratio." Much like the Sharpe Ratio, but instead of using standard deviation as the denominator, we use the downside deviation instead. This is the annualized return (CAGR) minus the risk free rate (in this example, I set the risk free rate at 0) divided by the downside deviation. Higher numbers are better, because they indicate that an investor is being better compensated for risk taken. Over the test period, the S&P had a Sortino Ratio 0.6 of while the Alpha Momentum Strategy exhibited a Sortino Ratio of 1.87, or more than 3x better than Buy & Hold. **Advantage - Alpha Momentum.**