# Chapter 17 : Expected Market Return

Who knows what the future will bring

Anonymous

In the Capital Asset Pricing Model, Expected Market Return (Returns Expected by Investing in the Stock Markets), is probably the most important variable in computing the cost of capital.

The formula for calculating the cost of capital is as follows:

ra = rf + [ βa x ( rm - rf ) ]

Where,
rf = Risk-Free Rate
βa = Beta of the security
rm = Expected Market Return

Where expected market return incorporates the risk of investing in the market.

Most decisions about investment, whether for allocating capital in corporate finance or investment in securities, are made to earn excess returns over the cost of capital. Thus, the expected return on the market represents the additional return expected by investors to invest in the equity market versus risk-free government bonds.

It is the Market Risk Premium (Rm - Rf) over the risk-free rate that investors expect to receive from an investment in the market (a portfolio of index stocks), represented by market indices like the S&P 500 Index, Nasdaq, Nifty, Dow Jones, FTSE, etc.

The effect of a decision that the appropriate expected market return is 10% instead of 12% in the Capital Asset Pricing Model (CAPM), will generally have a significant impact on the computed value. For instance, if the Earnings Per Share (EPS) is 120, then discounting by 10% gives a value of 1200, and discounting it by 12% gives a value of 1000, a difference of 20%.

In this chapter, I will give you a model to estimate the expected market return based on a study of over 100 years of S&P 500 called Expected Returns over Inflation (ERI). Though you can use other models such as historical premiums or future expected returns based on analysts' forecasts to arrive at expected market return (EMR), I believe that the ERI method is simple and backed by data.

## Model for computing Expected Market Return (Rm)

The ERI model for computing expected market return is Expected Inflation Rate + Expected Returns Over Inflation.

A study was conducted to determine the Real Return (market returns plus dividend yield less inflation) for the S&P 500 for over 100 years, and it revealed the following:

• The Compounded Annual Growth Rate (geometric average) of real returns was 6.9% from 1914 to 2021.
• Then, for each sequence of 30+ years from 1914 onwards till 2021, the median was 6.9% with a standard deviation of 1%. The maximum returns were 8.59% and the minimum was 5.66%.

Expected Market Return is Expected Inflation Rate Plus Expected Returns Over Inflation.

Though the market may price the index based on numerous factors on a day-to-day basis or year to year basis, the prime assumption here is that in the long-term, the returns will have a mean reversion.

Thus, if we assume an expected inflation rate for India to be 5% and add 6.9% as the expected returns over inflation then the expected market return for India is 11.9%. Similarly, if we assume the expected inflation rate for the US to be 1.5% and then add 6.9%, we have expected market return for the US to be 8.4%.

### Computation of EMR in the example of Black Bay Pizza

In the example of Black Bay Pizza, I have assumed the expected inflation rate to be 5% and the expected return over inflation at 7%. Thus, the expected market return is 12% (5% + 7%).

## Inflation and Duration

It is nearly impossible to predict inflation over a long duration, thus the cash flows and the cost of capital. However, all three have a direct correlation to inflation. If we assume the inflation to be 2%, then we generally assume, in the long-term, that cash flows will have an inflationary impact of 2% (discounted cash flows assume that a company is a going concern and has a life to infinity).

Similarly, the risk-free rate should assume an inflation of 2% and the expected market return should be assumed with 2% inflation.