## Wednesday, July 17, 2013

by Suyash Rai.

### What is the Equity Risk Premium and why it matters

The basic intuition in investing is that over and above the time value of money, the return on an investment must compensate for the risk it adds to the portfolio of an investor. In the Capital Asset Pricing Model (CAPM), this rate of return can be computed based on two variables: the risk premium of the market on the whole (ERP), and the sensitivity of an asset to the market (Beta). The asset must generate returns equaling the time value of money (a.k.a. the risk free rate) plus ERP*Beta. This tells us the required rate of return for an asset of systematic risk Beta.

The Equity Risk Premium (ERP) is a key variable in many decisions in corporate finance and asset pricing. The equity index is a diversified portfolio where the bulk of gain from (domestic) diversification has been accomplished. How much higher is the return on this portfolio, on average, when compared with taking zero risk by investing in government bonds? This value is termed the equity premium' or the equity risk premium':

$\textrm{ERP} = E(r_M - r_f)$

The equity risk premium is at the heart of finance, shaping the behaviour of everyone buying, selling or regulating publicly traded assets. For example, monopoly regulators the world over use some version of the CAPM to decide how much return is fair for regulated monopolies. The ERP is an essential component of this decision. For example, the Airport Economic Regulatory Autority (AERA) uses the standard CAPM to determine the fair rate of return on capital for private airports in India. All these applications require arriving at a numerical estimate for the ERP.

### A warning about the risk free rate

Estimating the ERP inherently requires taking a stand on what the risk-free rate is. For the risk free rate, the yield on a government of India bond can be used. For short-term decisions, treasury bills (maturity of under 1 year) can be used, but for most decisions with long term horizons, it makes sense to use yield on the 10-year government of India bonds. The 10-year bond has a deeper, more liquid market, and therefore provides a more reliable estimate of the risk free rate, compared to government bonds of other maturities.

We have to, however, keep in mind the problem that under the Indian system of financial repression (forced purchases of government bonds), the observed interest rates on all government bonds are understated: given the level of inflation, default risk and inflation risk in India, voluntary buyers would require a higher rate of return.

In the future, many things are likely to happen to the risk-free return in India. Progress on easing financial repression will remove the forced purchases of bonds and tend to push up the required rate of return for government bonds. On the other hand, access to the Indian bond market for foreign buyers of bonds will give lower interest rates. Finally, establishing a sound central bank, as envisaged under the draft Indian Financial Code, will give low and stable inflation which will give a lower cost of borrowing for the government.

Another problem is that prior to 2000, market data on the government bond market is highly spotty. Some analysts (for example, see this paper by Prof. Rajnish Mehra) use the bank deposit rate as the risk free rate in the pre-2000 period. However, this is also a rate that was distorted by regulation and did not reflect market forces.

### Three alternative approaches for estimating the equity risk premium

Even though the ERP is extremely important, it is quite difficult to arrive at a good numerical estimate for it. There are three stylised approaches of estimating ERP, each with a few variations (for a detailed discussion on these approaches, see this review paper on ERP). They are:
2. Utilising forward looking estimates
3. Looking back

In this article I review these three approaches as a mechanism for estimating the ERP in India, and offer some views on what the most sensible estimates might be.

### 1. Asking around

If two alternative estimates are unbiased and imperfectly correlated, then a combination of these estimates is generally better than either of the two. Hence, we can survey investors, portfolio managers, and other people we consider relevant, and ask them about what they think is a reasonable spread of stock returns over time value of money. The average value will be a good estimate as long as each person has an unbiased estimate.

A recent survey (published on June 26, 2013) of 12 finance and economic professors, analysts and managers of companies in India found the average ERP to be around 8.5% (up from 8% in 2012).

This method is used by many practitioners, but its validity is quite suspect. There is a great degree of recency bias in ERP based on surveys, and given the voluntary nature of responses, we usually don't know how representative the surveys are. If the survey respondents are not using a sound basis for estimating the ERP, the survey cannot, in most cases, give an accurate estimate.

### 2. Looking into the future

One can compute the ERP implied in the present stock valuations and forecasted earnings for firms. The implied return is calculated based on the stock valuations and the forecasted earnings, and then the risk free rate is deducted.

This implied ERP can change quite rapidly, because it is based on the current stock valuations and expected cash flows. For example, in the US, implied ERP (based on Free Cash Flow to Equity or FCFE) was 2.05% in 1999, and doubled to 4.10% in 2002. Someone using the 1999 implied ERP to take a decision with, say, a ten year horizon, would have underestimated the risk premium. A variant of this method, which mitigates this problem, is to take the average implied ERP for the last few years.

To calculate the implied ERP, we require estimates of future cash flows, which, except for a few well-analysed firms, may not always be available. In India, we now have a number of analysts regularly putting out earnings estimates. For the biggest firms in India, there are 20-40 such analyst reports available at any point of time. But for most other firms, these estimates are hard to come by. Taking a handful of prominent firms as representative of the entire market may lead to an under-estimation of risk premium.

The strength of the implied ERP approach is that it yields a reasonably good estimate of the ERP over a short term (over the next few years). For June-end, 2013, one estimate of the implied ERP (by Pitabas Mohanty of XLRI) is 10%.

### 3. Looking back

The most commonly used method for estimating the ERP is the historical method. This method uses the difference between the average historical return on a stock market index and the returns on the riskless asset. It is a useful method in many contexts, because it yields a good estimate of the long term central tendency of the ERP. However, it has big problems in the Indian context. Two problems stand out: the problem of estimating risk-free rate, and the shortage of historical data on index returns.

We don't have a long span of equity market data available. Though the index returns (on BSE Sensex) are available from 1979 onwards, dividend data in CMIE Prowess only starts from 1990. So, we have reliable data on market returns for about 23 years only (1990-2013).

The full time-series for the BSE Sensex, from April 1979 onwards, has 8100 observations. However, estimating average returns depends only on the span and is not helped by frequency. And the span of only 23 years in the period where dividends are observed, leaves a lot to be desired. The average annual return on BSE Sensex (not including the dividend yield) during this period (July 06, 1990 to July 05, 2013) is about 19% and the annualised standard deviation of daily returns is 27.8%. As a consequence, the mean return is estimated quite imprecisely: the standard error of the mean works out to 5.8%. The 95% confidence interval runs from 7.4% to 30.6%.

A few more years of data is not going to solve this problem. Halving the standard error requires increasing the span by 4 times.

Let's apply the basic historical method of estimating ERP in India. As the risk free rate, I take the average yield from 2000-01 to 2012-13 on the 10-year government of India bond: 7.77%. The average total annual return on the Sensex (stock return+dividend yield) from 1990 to 2013 is 20.7%, but this is an arithmetic mean. For equity returns, geometric mean is a better measure of central tendency, because of the high level of serial correlation in the series of market returns. The geometric mean of total annual returns (stock returns+dividend yield) is 15.9%, which means that the historical ERP is 8.13%. This is an estimate, but not a reliable one.

### 3a. Looking back in a different way

To work around the problems in the historical method we need to use a variant of the historical method, which helps us make the most of the advantages of the method, while overcoming the measurement limitations we face in India. This can be done if we take the historical ERP for a mature market (or a group of mature markets) over a long span, and adjust it for the premium to be paid for India's country risk. In using this method, the best option is to take long run historical ERP from the US as the base. Stable and reliable equity market time series is available for a fairly long span in the US. Based on equity market returns from 1928 to 2012, the historical ERP for the United States is 4.2% (geometric mean). Adjusting for the country risk premium for India is a bit tricky. It can be done through a number of methods, each with its pros and cons:

1. Based on sovereign rating: There is a default spread implied in India's sovereign rating. India's sovereign rating of Baa3 (Moody's) implies a default spread of 2%. Based on this the ERP in India is 4.2%+2% = 6.2%.
2. Based on bond spreads or CDS spreads: Bond spreads and CDS spreads are often used, but the relevant information is not available for India. For bond spreads, we need a significant amount of sovereign debt denominated in US dollars, which is not there. There is negligible CDS activity on sovereign debt, mainly because very little sovereign debt is held by foreign investors.
3. Relative standard deviation of the Indian and a benchmark equity market: Another method is to use the relative standard deviation of India's equity market with the US equity market over the last few years. The idea in this approach is that since the standard deviation of returns is a measure of the risk in a market, the relative standard deviation can be used to adjust the mature market ERP to get the ERP in India. In this approach, the relative standard deviation of equity markets in the two countries is multiplied into the ERP of US markets, to get the ERP in India.
$\mathrm{ERP}=\mathrm{Default spread implied in sovereign rating}*\left({\mathrm{SD}}_{\mathrm{India Equity}}/{\mathrm{SD}}_{\mathrm{US Equity}}\right)$
Based on the relative standard deviation of equity returns from Feb 2011 to Feb 2013 (0.99), the ERP in India would be around 4.16. So, as per this estimate, the ERP in India is lower than that in the US. It is difficult to make the case that India is less risky than the US, and should have a negative spread vis-a-vis the US.
4. Relative standard deviation of domestic equity and bond markets: Another market-based approach is to use the relative standard deviation of the domestic equity and bond markets in India. The intuition in this method is that the default spread implied in the sovereign rating does not fully capture the risk of the equity market, and should therefore be adjusted to reflect the relative risk between the equity market and the debt market. The relative standard deviation is assumed to be a measure of this adjustment. In this approach, the relative standard deviation is multiplied into the default spread implied in the sovereign rating, and added to the mature market ERP.
$\mathrm{ERP}=\mathrm{Mature market ERP}+\mathrm{Default spread implied in sovereign rating}*\left({\mathrm{SD}}_{\mathrm{Equity}}/{\mathrm{SD}}_{\mathrm{Bond}}\right)$
Though in theory this is a good method, in application it gives strange results in some contexts. It is highly dependent on recent data on relative volatility. For example, right now in Greece, given the volatility in debt markets, this approach yields a very low ERP, lower than most developed markets. As of March 2013, India had the highest relative standard deviation of equity and bond markets in the world (4.91), more than many countries usually assumed to be riskier. This is based on two years of weekly returns. I think this high relative standard deviation is because of the relative inactivity in the bond market, which is largely dominated by sovereign bonds that are largely held by captive investors. Volatility in the market would increase if it becomes more vibrant. At present, this method yields an ERP of 4.2% + 4.91*2 = 14.02%.

Any historical method has two general problems: there is a certain degree of survivorship bias in the time series, and the ERP is obtained mainly on the basis of data from firms above a certain size. These biases need to be considered before using any version of the historical method of estimating the ERP.

### Choosing a suitable approach

There is no perfect method for estimating the ERP in India, and there is a wide range of estimates (from 4.16% to 14.02%). While choosing the suitable approach for our purpose, we must be cognizant of the fact that in the Indian environment, too often, we are flying blind with weak information. We don't have access to a long span of reliable market data. We don't have reliable estimates of future cash flows for many firms. We don't have reliable sovereign bond and CDS spread information. We don't have good indicators of the risk free rate. But we must make do with what we have; we have to go to war with the data that we have got.

I am thinking mainly about the corporate finance decisions. In corporate finance, the main use of the ERP is to estimate the cost of capital or reasonable rate of return on investments. In such applications, the ERP estimation method one uses is shaped by the horizon. For estimating the long run ERP (say, for more than 5 years), all methods other than the historical method are rife with problems, especially given the data availability in India. The standard historical approach is not suitable, because we really need a much longer span of equity market data, and much better indicators of the risk free rate.

A variant of the historical method can be used: one that takes the ERP from a mature market and adjusts it for India's country risk. In my opinion, for estimating the long run ERP, it is best to take the historical ERP for US, and add to it the default spread implied in India's sovereign rating. This yields the ERP of 6.2%. The other methods of adjusting for country risk premium suffer from serious problems. As of now, the two methods based on relative standard deviations yield very strange estimates, and therefore must be set aside. The ERP in India yielded by one of these methods is lower than the ERP for the US, and the other method puts the ERP in India at a level higher than many economies that are known to be much worse than India. Having regularly observed the results of these methods over the last few years, I have seen them yield some really wonky estimates of the ERP for many countries. We should use these methods carefully. The implied default spread, on the other hand, is a bit too stable (ratings are revised infrequently), but it is not as prone to absurd results.

So, I would say that 6.2% is a reasonable estimate of the long run ERP in India. If the horizon of asset pricing decision is long, this should be a reasonable estimate of the ERP in India. Take the example of the Airport Economic Regulatory Authority (AERA) of India, which needed an estimate of the ERP over a long horizon (5 years). We at NIPFP worked with AERA to estimate a reasonable rate of return for the private airports, and after due consideration of the options, AERA decided to opt for this method of taking the ERP from the US and adding to it the default spread implied in India's sovereign rating (see this order on the tariff for the Mumbai International Airport).

If the horizon of the investment decision is shorter, one needs an estimate of short run central tendency. In such contexts, one can use survey-based or implied ERP. The ideal survey should have a large sample that is drawn randomly from the surveyed population so as to be representative of it, and for implied ERP, reasonably reliable data on expected cash flows for firms should be available. Since it forces us to do our own math and to think precisely, and because good data is now available for firms in India, I would say it is better to use the implied ERP than to use the survey-based ERP in India.

LaTeX mathematics works. This means that if you want to say $10 you have to say \$10.