Investment statistics is an extremely large topic but lets boil it down to the measures and explanations that we use and that are most important to us. You will not require a mathematics degree to understand the following.

When you research an investment, and we sincerely hope that you do research investments, you may have heard the following sentence

**"This investment has a CAGR of 25% and is expected to return in excess of 22% next year with a standard deviation of 16%"**

One of the most misleading statistics used by investment managers today is that of past performance and expected return.

**Annual Returns**

When you see an investment, usually some sort of managed investment, it should always have its past performance shown. Be careful! I am about to illustrate how there are several ways of measuring a return on investment and depending on the context it is used, it can be misleading. Returns are often expressed in terms of % return per year and sometimes its shown as rolling returns, 3 month, 6 month, or some other time period. This shows what the percentage gain in the time shown, so a 3 month rolling return highlights the return during the most recent 3 month period.

These rolling returns are used to show how the investment is performing in its most recent history.

It is rare that an investment would have this as a measure as it opens their performance up to more scrutiny. You tend to see this as a indicator only if the investment has performed well recently.

Sometimes it is shown as an Annual Return and other times its shown as an Annualized Return or Compound Annual Growth Rate.

An Annual Return is calculated as the total of each single year divided by the number of years.

Annualized Return is the smoothed and compounded rate of return would have been needed to arrive at the same end investment amount.

Where this can present some false information is when…

e.g. An investment over 4 years are 20%, -10%, 100%, 50% = 40% annual return

But the CAGR for the same investment is actually 34.2%.

Some funds managers choose to show the higher value.

The compound annual growth rate (OTCPK:CAGR) is a very common measure as it can be used to project what may happen to the investment if it can stick to its current return levels.

As an example, if we made 5% in JAN and 5% in FEB. Then we could draw a long bow and say that we expect to make 5% every month, therefore we'd have a CAGR of 60% (12 x 5%).

I'm sure that you can see the flaw in that metric. What if I didn't make 5% every single month?

If I were a shrewd fund manager, I would project a CAGR based on my best performing period in recent time. Of course, it's not always in the best interests of the investment manager, to show exactly what has happened. This explains the use of certain measures and statistics.

Generally, fund managers are required by government to show certain measures but you may need a magnifying glass in order to find them.

Some tricks that they use include:

- Showing a longer time period return, when the recent history has been poor.
- Projecting a CAGR based on a small number of months performance.
- Show an annual return vs. an annualized return if the early years performance was poor.

**Probability**

It is impossible to predict what an investment will do in the future. We can only rely on what has happened in the past to give us some guidance. This is why the analysis of investment statistics focuses on probability.

Sure, toss a coin in the air and we'd have a 50% chance of guessing what will happen. But what actually happens is random - we cannot predict it. You might get heads come up 12 times in a row.

Who knows?

When we look to compare investments with each other, we are using probability theory and are trying to come up with investments that are more probable to return what we want.

By the way, you may not always want high returns. You may require lower risk investments to stick to your asset allocation rules. Either way, when you research you are looking for the investment most likely to fulfill your investment requirements.

Another common way to compare an investment is with its standard deviation. This is the measure of how its history of returns (or risk, or other measure) is distributed around the mean. The mean being the average of the returns.

This is a measure of volatility or its variability. Since each month, the S&P index can have differing performance; it's said to be variable. But not as much as a derivatives fund. That fund would have a higher standard deviation as its volatility is higher.

If we say that the S&P index has a average return of 16% over the past 15 years, then we can show that its standard deviation is also about 15.4% with a 5 year average return of -0.14%.

Obviously, the past five years have not been good for this index.

Using Yahoo Finance, you can look up a mutual fund and see its Risk measures. So if I pick the Matthews Korea fund (http://www.matthewsfunds.com/), it shows a 5 year standard deviation of 29.36% at an average return of 20.56%.

The comparison is simply that the Matthews fund is more volatile, but has a better return. Other than that, you cannot compare their 2 investments any further. When you read further, you'll see that the Matthews fund is actually safer.

**Drawdown**

Nobody likes to lose money, especially after experiencing a rise. The drawdown is a measure from the highest point of an investment to the lowest point.

If you start with $10,000 and over the course of an investment, your investment rises to $12,000 then drops to $6,000. Then many people would think they have really lost $6,000 not $4,000.

Drawdowns of greater than 50% are quite large. They require a gain of 100% just to get back even.

Equally, if only small gains are made, it only takes a small fall to create a large drawdown.

**Risk Adjusted Measures**

Skewness is a measure of the bias of monthly returns. If the investment has a majority of monthly returns that are positive, then it's said to be skewed to the right of the normal curve. Conversely, if the majority of returns are negative then it is skewed to the left of the normal curve. Skewness figures that are positive and higher are best.

Kurtosis is a measure of the size of the odd monthly returns either side of the mean. In other words, how "peaky" are the returns. Sometimes investments have very large gains or losses, compared to their normal monthly returns. Look for Kurtosis figures to be positive and large.

Sharpe ratio is a measure of an investments reward compared to risk. How well has this investment performed against a benchmark and it's standard deviation. The higher the Sharpe ratio, the better the investment returns have been relative to a benchmark. This is usually the cash rate (approximately 3%)

With our two examples: Matthews Korea fund = 0.70 & S&P Index = -0.26 : showing the Matthews fund to be a far better performer - even given it's volatility. What does this mean when it comes to making comparisons?

If you look at the risk adjusted returns of the S&P index, then look at some very high performing hedge funds, you will probably notice that you'd have a much greater probability of earning higher returns if you invested in hedge funds. Even though they might seem riskier, their history shows a better-managed performance.

Isn't that what we want in the first place?

**Bottom Line**

- When you look at the performance history of an investment, try and determine the basis for their measure of performance.
- Understand that the past performance of an investment doesn't mean it will continue that same pattern in the future.
- Don't compare investments on expected performance and standard deviation alone without looking at their risk adjusted measures.
- An investment with a large drawdown doesn't always make a bad investment
- Risk adjusted measures can be more meaningful than expected returns

Of course taxation hasn't been a consideration at this point.

**Murray Priestley** - Chairman of Alpha Asset Managers, a provider of sophisticated fund management and trading systems to regulated investment managers and institutions around the world.. Alpha is a market neutral specialist that provides management and software services for professional and institutional investors. For more information, www.alphamgrs.com