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Tuesday, March 20, 2007

Indian Stock Market – Risk Vs Returns

Indian Stock Market – Risk Vs Returns

 

The euphoria of the 5-year Bull Run has been dampened by the recent slump in the BSE Sensex. Sensex has lost close to 7% of its value in just 1 month. It is reminiscent of the fall last May. General wisdom is to buy & hold, as over a long term stock markets provide the best returns. But is “general wisdom” really true?

 

I am sure if you had bought shares of Reliance in the 80’s or Infosys in the 90’s you would be millionaire many times over by now. However, what I wanted to know was how the markets on whole have fared over the last decade or so.

 

I had seen a chart at Fund Advice discussing returns using S&P. I wanted to do similar analysis for Indian markets. As a proxy for the markets, I used Sensex (well because the data was readily available and NSE Nifty is also similar). I was able to get data starting from Jul ’97 from Yahoo. Further from BSE I was able to get the data starting from Jan ’91. From these 2 sources I had daily close of Sensex from Jan 1, 1991 to March 09, 2007.

 

Once I had the data then for each given day I calculated the returns for 1, 3, 5, 7, 10 & 15-year periods. Once I had calculated for each day I then calculated the average returns for each period.

 

I am tabulating the result of all this number crunching.

 

Number of Years

1 Year

3 Year

5 Year

7 Year

10 Year

15 Year

Average Annualized Return

19.99%

11.74%

7.65%

6.67%

6.66%

14.36%

 

The table provides the average returns an investor would typically see. What is surprising is that as the years go up returns decline all the way down to Year 10. This directly contradicts the “general wisdom”, at least for the Indian Markets. Ignore 15 years returns as they are for only 2006 & 2007, which has been a bull market. To have realistic annual rate of return we should look at 10-year returns, this includes the current bull market and severe bear market from mid 2000 to 1st quarter of 2003.

 

The problem with average return is that it can be skewed by outliers i.e. data which is either too high or too low. Also, the probability of such outliers is usually low. Therefore, another way to look at the returns is to look at the Median.

 

Number of Years

1 Year

3 Year

5 Year

7 Year

10 Year

15 Year

Average Annualized Return

19.99%

11.74%

7.65%

6.67%

6.66%

14.36%

Median Annualized Return

11.99%

6.02%

5.41%

6.66%

5.54%

14.16%

 

The interesting thing to note about median returns is that it approaches the average as the year progresses. What this tells us is that as number of year increases volatility of returns decrease. Another way to look at this that we can be pretty sure that we would get approximately 6.66% returns on a 10-year investment. However, we may not get 19.99% returns in 1 year, as outliers skew data.

 

However, returns are just one aspect of investing. Another, more important aspect is the risk taken to get those returns. Risk is generally represented by Standard Deviation, which I calculated for each of the 6 different periods.

 

Number of Years

1 Year

3 Year

5 Year

7 Year

10 Year

15 Year

Average Annualized Return

19.99%

11.74%

7.65%

6.67%

6.66%

14.36%

Median Annualized Return

11.99%

6.02%

5.41%

6.66%

5.54%

14.16%

Risk (Std Dev)

40.16%

17.89%

9.81%

6.68%

4.71%

1.47%

 

This provides a confirmation of what was indicated by the median returns. One-year returns are highly volatile whereas 10-year returns are practically guaranteed. Again, it would be wise to ignore 15-year data as it contains data for 2006 & 2007, which has been a bull market.

 

Assuming the returns as a normal distribution, standard deviation (or risk) also tells me there is 68% chance that my 1-year return would range from –20.17% to 60.15%. It is likely (32% chance) that my 1-year returns can be out of this range. It also tells me that there 95% chance that my 10-year return will vary from –2.76% to 16.08%. There is a slight chance (5%) that my 10-year returns would be out of this range. It would be best to ignore the results of 15-year period, as there is not enough data for that period.

 

Number of Years

1 Year

3 Year

5 Year

7 Year

10 Year

15 Year

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Annualized Return

19.99%

11.74%

7.65%

6.67%

6.66%

14.36%

Risk (Std Dev)

40.16%

17.89%

9.81%

6.68%

4.71%

1.47%

Range (68% Prob)

-20.17%

60.15%

-6.15%

29.63%

-2.16%

17.46%

-0.01%

13.35%

1.95%

11.37%

12.89%

15.83%

Range (95% Prob)

-60.33%

100.31%

-24.04%

47.52%

-11.97%

27.27%

-6.69%

20.03%

-2.76%

16.08%

11.42%

17.30%

Range (99% Prob)

-100.49%

140.47%

-41.93%

65.41%

-21.78%

37.08%

-13.37%

26.71%

-7.47%

20.79%

9.95%

18.77%

 

(The above results are directly from the definition of standard deviation in a normal distribution. According to this definition 68% of the population lies between +/- 1 standard deviation, 95% of the population lies between +/- 2 standard deviation and 99% of the population lies between +/- 3 standard deviation.)

 

Finally, another way to look at the risk & reward is to look at the worst and the best performance in a given period.

 

Number of Years

1 Year

3 Year

5 Year

7 Year

10 Year

15 Year

Average Annualized Return

19.99%

11.74%

7.65%

6.67%

6.66%

14.36%

Median Annualized Return

11.99%

6.02%

5.41%

6.66%

5.54%

14.16%

Risk (Std Dev)

40.16%

17.89%

9.81%

6.68%

4.71%

1.47%

Min Returns

-50.99%

-18.18%

-8.02%

-7.39%

-2.80%

8.71%

Max Returns

264.77%

62.44%

36.03%

20.95%

17.38%

16.63%

 

It is interesting to note that for 5, 7 & 10-year periods the max & min fit approximately within 2 standard deviation of the average returns. Also note the outlier for 1-year return.

7 comments:

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