The idea of a risk premium is one of the most important investing concepts essential for those who invest in volatile assets and those who shun them as too 'risky'.

The definition of a risk premium is fairly simple. If a risk-free instrument offers say 7% return, what is the return I should expect for the risk I wish to take? Or in other words, what is the return I expect? If this is 10%, then risk premium is simply 10% - 7% = 3%. In other words, the risk premium is the expected compensation for the risk taken.

Very few investors realise that the risk premium is also the money lost when an investor decides to invest in a risk-free asset. For example, when we invest in a bank FD at 6-8%, what does the bank gain from it? It lends the money at a much higher rate to corporates.

Did you know that the central government does the same with our PPF and SSY and other small saving schemes money? It lends it to our states at a 'premium' of about 2%. Did you think these schemes are EEE for *our* benefit!!

Take LIC (or any other insurer). It invests a part of the money obtained via traditional policies and invests it in the stock market. Part of the bonus given to policyholders is from capital gains obtained by booking profits from time to time.

The point I wish to make is, when we choose to avoid risk, someone else will profit from it. This is the premium we pay.

In other words, risk premium cuts both ways. If we choose to take a risk, we *may be *adequately compensated. If we choose not to take a risk, we *have to pay compensation.* There is no free lunch.

By directly investing in stocks, bonds, gold or any product that is valued at market price each business day, we are eliminating the middlemen - banks, insurers, the government etc. This gives a shot at earning more.

Now, assuming that we do choose to invest in volatile instruments directly, it is important to recognise that the volatility does not reduce with time. Equity mutual funds are commonly mis-sold and mis-bought by saying that returns will be "good" over the long term. The implication of that statement is risk will reduce if we stay invested through thick and thin. This is absolute rubbish.

**Want proof? Read more:**

Understanding the Nature of Stock Market Returns

Will long-term equity investing always be successful?

Dollar Cost Averaging aka SIP analysis of S&P 500 and BSE Sensex

Take the case of those suggest investing "more" in small cap, micro cap and nano cap mutual funds. The assumption here is that the volatility does not matter over the long term. Again a baseless assumption.

By assuming risk will reduce to such an extent that there would be no capital loss over the long term, we are assuming that the return from equity would be practically risk-free. Such a notion is extremely dangerous.

**What is risk?!**

A positive risk premium means little. If I get a return of 9% over a risk-free rate of 7%, the risk premium is 2%, but real life inflation is often much higher than 9%. So there is not much to rejoice.

The traditional definition of a risk premium is of limited use in countries where actual inflation is in double digits. The change in cost inflation index or wholesale price index is of little relevance to how we run our lives.

**Measuring risk premium**

If I know the risk-free return and the expected return, it is trivial to calculate the risk premium. However, risk premium per se does not make any sense without the actual return obtained.

A risk-free return is usually a fixed income asset which offers interest on the amount invested and then interest for the interest and amount. That is the classic definition of compounding applies. The interest offered each year is the same (say 7%).

So after say 5 years, Rs. 100 invested becomes

100 x (1+7%) x x (1+7%) x (1+7%) x (1+7%) x (1+7%)

or 100 x (1+7%) ^5 - the classic compound interest formula.

However, a market linked instrument does not interest and one cannot apply the above formula straight away.

Instead one calculates growth (or lack thereof) each year.

For example, Rs. 100 invested became Rs. 140 in one year and that amount reduced to Rs. 120 after one more year and so on.

Or in other words, 40% growth = return in the first year, -14.3% return in the second year and so on.

Therefore, I can write,

100 x (1+40%) x(1-14.3%) x (1+10%) x (1+19%) x (1-6%) = 147.63

Now this is messy. I can replace the above equation by

100 x (1+ R) = 147.63

This R is the *average growth in our investment year upon year *and is known as the compounded annualised average return (**CAGR**). That is we are replacing the volatile annual rates of growth by a single rate of growth.

Had our investment grown *at the same rate of growth *year after year for 5 years, Rs. 100 would have become Rs. 147.63 with R = CAGR = 8.10%.

Many people make the mistake of assuming that 8.10% is the actual yearly growth rate. It is not. Each year's growth rate has fluctuated violently as shown above.

The key takeaway is, we need to replace the various growth rates by a single growth rate to enable comparison with the risk-free rate. Without the CAGR, we will never know if our investment has beat a risk free investment or not. The risk premium will not have any meaning.

**Read more: ** Understanding Annualized Return: CAGR and XIRR

kamalgarg1958Nice insightful post on risk premium, volatility and CAGR.

ABA post on very fundamental subject...Appreciates your efforts for educating us....!!

Parshwadeep LahaneExcellent post ! Basic knowledge upgrade. Thanks Pattu !!

Sriram RBrilliant post. Thank you.