How Risk-Adjusted Approaches Can Save you from
Financial Traps

What is Risk-Adjusted Return?

Risk-adjusted return is a professional’s way to evaluate an investment opportunity. Asking, ‘how much risk do I need to take to get those returns?’ sums it up.

The key here is ‘risk’, which is subjective. Glyn A. Holton (2004) talks about risk in his research and says that jumping out of a flying aeroplane without a parachute is not risky - death is certain.

In other words, risk is the probability of an event, which is different from certainty.

Risk = uncertainty + exposure

There are financial measures for investment risk assessment and risk identification such as; standard deviation, alpha, beta, R squared, Sharpe ratio and ulcer performance index.

1. Standard Deviation

Standard deviation measures the dispersion of a data-set relative to its mean. It is calculated as the square root of variance and depicted in percentage points or ‘pp’.

The key word here is dispersion. For example in mutual funds ‘dispersion’ represents how much the return on the fund is deviating from expected normal returns.

Simply put, standard deviation measures risk.

Low standard deviation (low risk) means that the data points (or performance of a fund) is close to the mean (expected return), while high standard deviation (high risk) value indicates that the performance is volatile - it fluctuates (as the data points are spread over a wider range).

Let’s look at an example. Say, you have a choice between two stocks A and B.

In the past 20 years...

Stock A had an average return of 10 per cent with standard deviation of 20 pp, while stock B had an average return of 12 per cent with a standard deviation of 30 pp.

By simply looking at risk and return, Stock A seems safer since B's additional return of two percentage points is not worth the additional 10 pp of standard deviation.

Moreover, Stock B is likely to lose the initial investment (but also to exceed it) more often than Stock A, but on average it is estimated to return only two per cent additional.

Another way to look at the returns is, Stock A is expected to earn around 10 per cent, more or less 20 pp (between 30% and −10%), while Stock B is expected to earn around 12 per cent more or less 30 pp (between 42% and -18%).

2. Sharpe Ratio:

Sharpe ratio examines the performance of an investment by adjusting for its risk. The following is the mathematical formula for Sharpe ratio.

Sharpe Ratio = Compound Annual Growth Rate - Risk Free Rate

Annual Risk

Compound annual growth rate (CAGR) is what you normally hear fund managers boasting about on blogs and YouTube. However, in the Sharpe ratio, we integrate risk to see exactly what the earning has been. The risk-free rate is usually the U.S. treasury rate.

Notice in the denominator (the bottom part of the fraction) the annual risk is the standard deviation. If this number gets bigger, it would indicate that risk is highly volatile. Also, the ratio itself will reduce as the denominator increases.

Let’s put in some values to understand what this ratio means.

CAGR = 12%

Risk Free Rate = 1%

Annual Risk = 11%

Sharpe Ratio = 12% -1% = 1


A simple principle (not a rule) is that Sharpe ratio of greater than zero means that the fund might be a better risk-adjusted choice than the risk-free rate. If the ratio is negative (less than zero), the risk-free rate might be a better option. And if it is greater than one, then it is a good choice as a risk-adjusted performance.

Generally, you should be looking for a higher than one value (Sharpe ratio > 1).

Another way to evaluate a fund from this same concept is that a fund should increase its returns more than it increases its risk. Or the numerator (top part) should increase faster than the denominator (bottom part) of the equation. Strangely enough, it is not that difficult to achieve.

Bull market is a blessing!

But the problem is that as soon as the market stops cooperating (when passive profits are hard to come by) the expected return start shrinking. Which is why the Sharpe ratio is a much better measure of performance than a simple return.

Let’s look at real life example as to how the Sharpe ratio can help assess the investment return better.

The following table shows the rate of return in the second column for XIV and SPY. XIV was the volatility index launched in 2010 and SPY is the symbol for S&P 500 ETF. Looking at CAGR, it seems that XIV would beat SPY convincingly.

Rate of Return (CAGR) Annual Risk (Standard Deviation) Sharpe Ratio
XIV (Inverse Volatility ETN) 37.9% 63.4% 0.57
SPY (S&P 500 ETF) 13.7% 11.4% 1.03

Comparison from 2010-2017

But when you look at the third column which lists the standard deviation, it completely flips the performance. To make sense of all of this, we calculate the Sharpe ratios for both products in the last column.

As mentioned before, Sharpe ratio of above one is preferred. And in this case, SPY is almost twice the ratio of XIV.

The higher the ratio the better.

Also, it indicates that SPY is far more consistent in its performance than XIV.

If you are still thinking why does it matter when XIV has better absolute returns? Here is the context.

If you flip a fair coin, you have a fifty/fifty chance of getting heads or tails. But if you flip enough times there will be some streaks where you get heads twice or thrice in a row.

Would you bet on heads more than tails simply because of that streak?

You shouldn’t. The chance of landing a head on the next flip is as much as of landing tails.

The point is that you shouldn’t base your investing decisions on streaks (short-term performance).

The XIV was launched in 2010, it had not seen the bear market. Relatively speaking, we never had its ‘long term’ performance.

A fund or investing product that has gone through a bull market and survived the bear market can demonstrate a consistency of performance better.

NOTE: After an 84% drop on 2/5/2018, Credit Suisse decided to terminate the Inverse VIX Short-Term ETN (XIV).

3. Ulcer Performance Index

The Ulcer performance measure is an improvement in the Sharpe ratio. On its own the ratio is good but it has a certain drawdown when it comes to measuring standard deviation; it treats gains and losses the same.

If you have some familiarity with the concept of standard deviation it is an objective measure of how much the performance oscillates from the mean; a gain of 15% is no different from a loss of 15% since both are simply deviations from the mean.

Ulcer corrects these.

Ulcer Index measures volatility based on price depreciation from its high over a specific look-back period. It is similar to measuring the Sharpe ratio but the key difference is that instead of integrating standard deviation it incorporates monthly losses.

So when there is a positive gain in a month, that is simply considered zero deviation for that month. In other words, it focuses on drawdowns.

Hence the name Ulcer performance index. The narrative is that stress causes ulcer, which is caused by investing losses. Therefore, it only accounts for the stress-inducing investing performance.

Let’s use the real example to understand how it works.

Rate of Return (CAGR) Ulcer Index (Standard Deviation) Ulcer Performance Index
XIV (Inverse Volatility ETN) 37.9% 30.5% 1.2
SPY (S&P 500 ETF) 13.7% 13.6% 3.4

Comparison from 2010-2017

In a similar situation as with the Sharpe ratio, the rate of return (CAGR) for XIV is impressive at 37.9% compared with the 13.7% return of the SPY. But as soon as you compare the two with the Ulcer Index, XIV seems extremely volatile with a higher percentage of drawdowns (30.5%).

How should an investor measure two products on the Ulcer Index scale? As with the Sharpe Ratio, the higher the Ulcer Performance Index (the last column from left to right), the better the product (delivers more consistent returns).

4. Alpha

Alpha is a risk evaluation measure that evaluates the active return on an investment. It reflects the performance of an investment in relation to an index or benchmark. The return in excess of the benchmark index is the investment’s alpha.

It is shown in numbers. Say a mutual fund has an alpha of 4, which would mean that its performance was 4% better than the index. Similarly, alpha of -3 would mean a performance of 3% worse than the benchmark.

5. Beta

Beta measures volatility (systematic risk) in comparison to the market as a whole. It is used in the capital asset pricing model (CAPM), which measures the expected return based on its beta and the expected market return. In risk analysis, it is also referred to as ‘beta coefficient’.

Usually, utility stocks have a beta of less than 1. On the other hand, most high-tech stocks (say on Nasdaq) have a beta greater than 1, which indicates the possibility of a higher rate of return but at higher risk. For example, Autodesk, Inc. (ADSK) - which is listed on Nasdaq - has a trailing beta of 1.67 (as of August 15, 2018).

6. R-Squared

R-squared measures the proportion of the variance for a dependent variable that is explained by an independent variable (how much the price of a financial security moves based on the movement of the benchmark index).

R-squared is normally perceived as the percentage of a fund's movement that can be explained by the movement of the benchmark.

For instance, an R-squared for a bond versus a bond index captures the bond’s proportion of price movement, which you can predict from the index’s movement. Similarly, you can use R-squared to predict a stock’s proportion of price movement based on the movement of the S&P 500.

How can you minimize the risks associated with investing?

Investment Risk Management:

You can minimize investment risk in many ways. First, you must identify risk, since the type of risk will define your course. And second, risk management will depend on your investment strategy - how one investor minimizes risk cannot be universally applied.

For instance, you may reduce your market risk by filtering out stocks with high P/E ratios or shaky management, or companies with volatile earnings and sales growth. But one person’s risk tolerance or style of investing might be able to afford exposure to volatile sales growth.

However, what you need most is the balanced approach to risk management. You decide which risk management process suits your investing goals.

Just like you have a choice between bottom-up approach risk management and top-down approach risk management.

In the bottom-up approach, you would pick individual stocks focusing on the performance of specific companies as opposed to making investment decisions based on macroeconomic indicators. The investor uses mathematical models, which are data sensitive, to analyze individual risks. It is more of a forward-looking approach.

The top-down approach is backward looking, which focuses on industries and sectors to achieve a balance in the portfolio. It studies the economic variable that is not explained by external macroeconomic factors.

Risk adjusted approach is a more refined way to investing. Accurately assessing risk can make investing and asset allocation much safer.

Work Cited

Holton, G.A.  2004. Defining risk. Financial analyst journal, pp. 19-25.

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