Risk is not always a bad thing
What is the second thing that strikes your mind when you hear the word 'equity' or 'stock'? (If 'risk' is the first thing that flashes across your mind, then you seem to have had an overdose of emphasis on risk in our recent school write-ups. Maybe it is time for you to learn more about how stocks offer great returns over the long run and the 'power of compounding'.)
If 'risk' is the second thing to take the dias, you are ready to take the next few steps in understanding this concept better. And just in case 'risk' was the last thing to chance upon your mind, we suggest that you start right at the beginning of these series.
If 'risk' is the second thing to take the dias, you are ready to take the next few steps in understanding this concept better. And just in case 'risk' was the last thing to chance upon your mind, we suggest that you start right at the beginning of these series.
What is equity risk premium?
Last time we understood that though risk is the chance of loss, it is equally a matter of choice. 'Equity risk premium' is the leveller that makes risky investment options attractive. Now it is time to put a finger on 'equity risk premium'.
We saw that Mr Savvy Investor settled for investing in the stock since he expected to make 13.4% extra returns over the 30% return on government bonds in three years. In other words, equity risk premium is forward looking.
If equity risk premium is forward looking and based on expectations, how do we know that we have settled for the right 'risk premium? Or how do we know that the 'risk premium' adequately compensates us in case the returns go against expectations?
A theoretically applicable method is to look at returns associated with all possible situations. Then assign probabilities to these possibilities and get a fix on the 'expected' return. In the end, the expected return needs to be compared with the risk-free return to evaluate if the 'risk premium' is adequate enough.
A little lost? Back to our good friend - Mr. Savvy Investor.
We saw that Mr Savvy Investor settled for investing in the stock since he expected to make 13.4% extra returns over the 30% return on government bonds in three years. In other words, equity risk premium is forward looking.
If equity risk premium is forward looking and based on expectations, how do we know that we have settled for the right 'risk premium? Or how do we know that the 'risk premium' adequately compensates us in case the returns go against expectations?
A theoretically applicable method is to look at returns associated with all possible situations. Then assign probabilities to these possibilities and get a fix on the 'expected' return. In the end, the expected return needs to be compared with the risk-free return to evaluate if the 'risk premium' is adequate enough.
A little lost? Back to our good friend - Mr. Savvy Investor.
Our thought experiment
Small Cement Company (SCC), Efficient Cement Company (ECC) and Big Cement Company (BCC) are three cement companies.
SCC has small capacity and hence its earnings improve dramatically after cement prices cross a threshold price. ECC, on the other hand, has a very efficient process and hence its earnings improve sharply with any rise in cement prices. The biggest of them all, BCC, is not so sensitive to cement prices, thanks to its size. In other words, BCC's bottom line moves in a more sober manner to the changes in cement prices.
SCC has small capacity and hence its earnings improve dramatically after cement prices cross a threshold price. ECC, on the other hand, has a very efficient process and hence its earnings improve sharply with any rise in cement prices. The biggest of them all, BCC, is not so sensitive to cement prices, thanks to its size. In other words, BCC's bottom line moves in a more sober manner to the changes in cement prices.
Time to make one simplistic assumption
Let us assume that the earnings of these companies are sensitive to only cement prices. Hence, cement prices determine the returns from investing in these stocks.
Mr. Savvy Investor needs to pick the best investment option from these three companies.
Luckily, a cement expert and a stock market analyst have made life for our friend a little simple.
The cement expert has assigned the following probabilities for the change in cement prices over last year. The stock market analyst has given his assessment of the expected returns from these three stocks for the respective changes in cement prices.
Mr Savvy Investor had to make a wise choice with just these details.
He calculated the average returns that he expected to make for each company. He had the probabilities associated with each return. Hence, all he had to do was multiply each probability with the associated return and add all of them together. For example, the average return that one can expect on SCC worked out to:
20%*-5%+30%*10%+40%*25%+10%*35% = 15.5%. This way, he calculated the expected returns for these three companies as follows:
Do you think the choice was very easy for Mr Savvy Investor? After all, he just worked out that SCC has the highest expected returns.
Think again, for our wise investor has chosen BCC over the others.
To find out why, cast a glance upon the main table again. The returns on SCC can swing from -5% to 35%, an extremely volatile stock indeed, with returns moving in a range of 40% from -5% to 35%. On the other hand, ECC is little less volatile as its returns fluctuate within a band of 0% to 30% - a range of 30%.
Finally, BCC is found to be a relatively steady stock. The worst case return on BCC is found to be 5% although the best case return, at 25%, is less than the returns of the other two. Anyway, this is a comparatively small range of 20% fluctuation in return.
Mr. Savvy Investor needs to pick the best investment option from these three companies.
Luckily, a cement expert and a stock market analyst have made life for our friend a little simple.
The cement expert has assigned the following probabilities for the change in cement prices over last year. The stock market analyst has given his assessment of the expected returns from these three stocks for the respective changes in cement prices.
| Event | Probability | Returns | ||
| SCC | ECC | BCC | ||
| 5% decline | 20% | -5% | 0% | 5% |
| Flat | 30% | +10% | +10% | +10% |
| 5% increase | 40% | +25% | +20% | +15% |
| 10% increase | 10% | +35% | +30% | +25% |
Mr Savvy Investor had to make a wise choice with just these details.
He calculated the average returns that he expected to make for each company. He had the probabilities associated with each return. Hence, all he had to do was multiply each probability with the associated return and add all of them together. For example, the average return that one can expect on SCC worked out to:
20%*-5%+30%*10%+40%*25%+10%*35% = 15.5%. This way, he calculated the expected returns for these three companies as follows:
| SCC | ECC | BCC | |
| Expected Returns | +15.5% | +14% | +12.5% |
Do you think the choice was very easy for Mr Savvy Investor? After all, he just worked out that SCC has the highest expected returns.
Think again, for our wise investor has chosen BCC over the others.
To find out why, cast a glance upon the main table again. The returns on SCC can swing from -5% to 35%, an extremely volatile stock indeed, with returns moving in a range of 40% from -5% to 35%. On the other hand, ECC is little less volatile as its returns fluctuate within a band of 0% to 30% - a range of 30%.
Finally, BCC is found to be a relatively steady stock. The worst case return on BCC is found to be 5% although the best case return, at 25%, is less than the returns of the other two. Anyway, this is a comparatively small range of 20% fluctuation in return.
Factoring in volatility of return
Mr Savvy Investor made another smart back of the envelope calculation. He divided the expected returns for each of these stocks by the range of possible returns. Look at what he got from his crude calculation...
In other words, Mr. Savvy Investor calculated his expected returns for every unit range of return that the stock could swing. A neat approximation to what the statisticians will call 'deviation from the mean'. BCC turned to have the highest return for every unit of risk.
The answer became obvious to Mr. Savvy Investor- BCC was the best investment option.
Of course, he might discover that the risk premium built into the 12.5% return from BCC' investment is not a good enough premium. But that is a different story altogether.
| SCC | ECC | BCC | |
| Exp Returns/Range | 0.3875 | 0.467 | 0.625 |
In other words, Mr. Savvy Investor calculated his expected returns for every unit range of return that the stock could swing. A neat approximation to what the statisticians will call 'deviation from the mean'. BCC turned to have the highest return for every unit of risk.
The answer became obvious to Mr. Savvy Investor- BCC was the best investment option.
Of course, he might discover that the risk premium built into the 12.5% return from BCC' investment is not a good enough premium. But that is a different story altogether.
A recap on this lesson
We will revisit these calculations later. It is time now to take stock of what we have learned about 'equity risk premium' so far:
- This premium is forward looking in nature, as it is based on 'expectation' of return.
- Expected returns could vary within a wide range. A higher range of return implies a higher gap between expected return and the actual return, thereby increasing the uncertainties associated with the return.
- We also understood that in case the range of returns from an investment in a stock is very large, then investing in the stock is more risky. However, this was a crude way of pinning the volatility of stock returns.
- After all the more likelihood of stock returns swinging from our expected returns, the more uncertain the actual returns we realise in the future. Look at our example, SCC returns are expected to be 15.5% but the eventual returns could swing any where from a -5% to 35% depending on how cement prices turn out.
- Statistically, the deviation from the expected return is a measure of the volatility of the stock returns.
- It is not enough to select the stock with the highest 'expected' return. It is important to select a stock that has a higher return per unit of risk.
Getting the 'risk premium' right - the next step
Now that we understand all these concepts, how do we get around the issue of obtaining a fix on this risk? After all, everybody invests based on expectations. How can we figure out today how much the returns will deviate from expectations in the future?
Academicians have worked on evolving methods that help us approximate and get a better fix on these future uncertainties. Next time, we will grapple with the issue of getting a fix on 'risk' and demanding the right 'risk premium'.
Academicians have worked on evolving methods that help us approximate and get a better fix on these future uncertainties. Next time, we will grapple with the issue of getting a fix on 'risk' and demanding the right 'risk premium'.
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