Market Risk & Risk Charts - An Investor's First Lesson
Team Latte
Aug 07, 2002

What is understood by risk, or more specifically market risk? How does one measure risk and how does it affect an investor, or a banker or a fund manager?

A widely accepted and common method of defining and measuring market risk is to estimate the volatility of the asset return. Volatility or more specifically historical volatility is best defined as the amount of variability in the returns of a particular asset. This is based on the actual movement experienced by the market in the past. Mathematically, such variability is measured by the Standard Deviation of the return. Very simply put, volatility implies how much the returns will deviate from an average value. Such an average value is estimated by calculating the mean annualized return of an asset for a period of time; and then this mean measure an investor's expected value on his investment in that asset. If an investor is expecting a 10% return from holding a particular stock then volatility will measure by how much will the actual return deviate from this expected value. (Please note that the actual return could be positive or negative.) The returns from an asset are assumed to be normally distributed, i.e. they follow a bell shaped curve as shown in fig 1.0. It is supposed to be symmetrical around the mean return, or the expected value of the return, and a negative deviation from the mean i.e. the curve on the left side of the mean measures the probability of risk. There could be a positive deviation from the expected value and negative deviation from the expected value, which is the essence of market risk.

Fig 1.0 shows a bell shaped curve for Hang Seng index daily returns from Jan 1996 to July 2002. This curve called the probability distribution of the asset return - which is more or less symmetrical around the mean. This probability distribution curve measures the probability of occurrence of a particular return and therefore forms an essential part of risk measurement. The distance from either side of the mean is measured in terms of the volatility of the asset returns. If £g is the mean annualized return for the Hang Seng index and £m is the annualized volatility then 66.66% of the entire curve in fig 1.0 is contained between the value μ + σ and μ - σ whereas 99% of the curve is contained between the values of μ + 3σ and μ - 3σ.

Fig 1.0

Therefore, we can say that there is a 99% chance that an investor's loss will not be more than (minus) three times the volatility of the index. This is because three times the volatility is the negative deviation from the expected value (of the investor) which is contained in the 99% area of the curve.

Let us look the example in a little more detail. (Let us assume that Hang Seng index is an asset in which an investor invests.) Let's take the index price from January to July 2002. We take the daily price and calculate the daily return for the entire period. Such a return is calculated by taking the natural logarithm of today's price divided by yesterday's price. The chart below shows the daily return for the period. Fig 1.1 shows the daily return of Hang Seng index from January 1996 to July 2002.

Fig 1.1

As can be seen from the chart Hang Seng index return has fluctuated wildly over the last seven months. This 'wild fluctuation' represents the market risk of investment in this index. And the way to quantify the 'wild fluctuation' or in fact any fluctuation in the index return is the volatility.

We, in fact took a longer time series the Hang Seng index prices from Jan 1996 to July 2002. From such a daily price series an average return, which is annualized, is calculated. Such an average return is equal to -0.075%. This is the average annualized value of the entire return series from January 1996 to July 2002 and represents the expected value of future return. However, the actual return in future may or may be equal to this return and in fact could deviate significantly from this expected value on either side, i.e. above or below this number. This deviation form the expected value is captured by the volatility, or in other words by the standard deviation of the returns. In our example the standard deviation of the returns of the Hang Seng index from Jan 1996 to July 2002 is 31.28%.

Another way of looking at this figure is that the volatility multiplied by the amount invested by the investor is the magnitude of a possible loss. In other words if an investor invests HK$1,000 in Hang Seng index then this $1,000 multiplied by 31.28% (volatility) is equal to HK$312.80. This is 66.66% possible loss that the investor should expect from this investment. Please refer to the probability distribution curve that we discussed above (fig 1.0). Thus there is a 99% probability that our investor's loss will not exceed more than HK$938.4, i.e. three times the volatility of the index multiplied by the amount invested. (Of course, he may make a profit of HK$938.4 from this investment, but then that is on the right side of the mean and represents a positive deviation from the mean and therefore not material to risk calcuilation.) But his market risk, the risk of losing money from the investment in Hang Seng index is encapsulated by this historical volatility of the returns of the index times the amount he has invested.

This volatility changes from month to month, depending on the gyrations of the index, or generally speaking asset prices. The annualized historical volatility in one month, in all likelihood, is different from the other month. The chart below in fig 1.2 depicts the annualized volatility from month to month over a six year period. This is a Risk chart. It shows how the volatility has behaved over different months and as can be seen there are months when the volatility peaked at around 100% (Russian debt default in 1998) and then again over 40% (after September 11 attacks).

Fig 1.2

In fact we can see from the above risk chart that volatility of Hang Seng index is in the long run bounded between 40% on the upside and 20% on the downside. Any move above or below this band quickly pushes the volatility back up pr down. (There could be important lesson in it for option traders, who buy and sell volatility.)

Further, look into the same period (Jan - Jul 2002) risk chart in fig 1.3 for the Dow Jones Industrial Average. It appears that volatility itself has bee fluctuating quite a bit between the range of 12% to 25%. Here also there have been peaks and valleys in the volatility chart.

Fig 1.3

A second kind of risk chart is the Relative Volatility movement. This measure the volatility of one asset class with respect to the other. For example below is a Relative volatility chart as depicted in fig 1.4 - of Hang Seng index and Dow Jones. The chart shows that with very rare exceptions Hang Seng index has always been more volatile that the Dow Jones and at time have been more than two times as volatile. In other words, to invest in Hang Seng has been more risky on a historical basis than investing in Dow Jones.

Relative volatility chart is important risk measurement for relative value investors. In table 1.0 the volatility and RiskGrade™ of all the major Asian indices (except Bombay Sensitive index) is shown RiskGrade™ is the trade mark of RiskMetrics Company and is a risk measure derived out of the annualized volatility. This shows the respective markets risks of each Asian index.

Fig 1.4

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