Risk Premium Formula

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Risk Premium Formula (Table of Contents)

Risk Premium Formula
Risk Premium Calculator
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Risk premium formula is calculated by subtracting the return on risk-free investment from the return on an investment. This helps to get a rough estimate of expected returns on a relatively risky investment as compared to that earned on a risk-free investment.

r_a = asset or investment return
r_f = risk free return

Various Types of Risk Premium Formula

Specific forms of premium can also be calculated separately, known as Market Risk Premium formula and Risk Premium formula on a Stock using CAPM. The former calculation is aimed at calculating the premium on the market, which is generally taken as a market index like the S&P 500 or Dow Jones. This is achieved by subtracting returns on a risk-free investment from a probable return on a similar investment in a specific market index.

The risk premium on a stock using CAPM is intended to help understand what kind of additional returns can be had with investment in a specific stock using Capital Asset Pricing Model (CAPM). The risk premium for a specific investment using CAPM is beta times the difference between the returns on a market investment and the returns on a risk-free investment.

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Risk Premium Formula Example

Person ABC wants to invest 100,000 US$ for the best returns possible. ABC has the option to invest in risk-free investments like US treasury bond which offers the low rate of return of only 3%. On the other hand, ABC is considering investment in a stock which can give returns up to 18%. To calculate the risk premium example for taking on the extra amount of risk involved with this stock investment, ABC would carry out this mathematical operation:

Risk Premium = r_a(100,000 x 18 / 100) – r_f(100,000 x 3 / 100) = 18,000 – 3000 = 15,000 US$

Hence, in this case, ABC enjoys a 15,000 US$ risk premium example with this stock investment as compared to the risk-free investment. However, it entirely depends on the performance of the stock and if the investment outcome turns out to be positive. For this, ABC would need to understand the risk factor involved by studying fundamentals of the stock at length and assess if this investment is worth it and whether he would be able to realize the risk premium or not.

Equity Risk Premium for US Market

Here, I have considered 10 year Treasury Rate as the Risk-free rate. Please note that some analyst also takes a 5-year treasury rate as the risk-free rate. Please check with your research analyst before taking a call on this.

source – bankrate.com

Market Risk Premium (RM – RF)

Each country has a different Equity Risk Premium. Equity Risk Premium primarily denotes the premium expected by the Equity Investor. For the United States, Equity Risk Premium is 6.25%.

source – stern.nyu.edu

Market premium = Rm – Rf = 6.25%
Rf = 2.90%
Expected Return from the Equity Market = Rm = Rf + Market Premium = 2.90 + 6.25% = 9.15%

Explanation of Risk Premium Formula

It is well known that generally speaking, stocks and bonds tend to have very different rates of return on the investment due to the inherent level of risk they have. Stocks, in general, present a lower level of risk and tend to generate lower returns as compared to return on the same investment made in stocks which have comparatively much higher risk, should the investment outcome be positive. Usually, US treasury bill, also known as T-bill, is used in the context of US-based investments.

However, it goes without saying that there is this additional risk of losing money in high-risk investments like stocks but what prompts one to make such an investment is the prospect of the additional return on such investment, as compared to the return on some risk-free investment. This is what premium formula helps measure.

Use of Risk Premium Formula

It must be carefully understood that market premium seeks to help assess probable returns on an investment as compared to any investment where risk level is zero, as in the case of US-government issued securities. This additional return on a risk-laden investment is in no way promised or guaranteed in this calculation or by any related factor. Should this investment outcome be negative, the premium calculation would have little relevance to that. It was the risk that an investor agreed to take upon in return for extra returns should the investment have a positive outcome. This difference between anticipated returns and actual returns that might be had on any investment must me understood clearly.

Risk Premium Calculator

You can use the following Risk Premium Calculator

R
a
f
Risk Premium Formula =

Risk Premium Formula =	R_a − R_f
	(0 * (0 / 100)) − (0 * (0 / 100) =	0

Risk Premium in Excel (with excel template)

Let us now do the same Risk premium example above in Excel. This is very simple. You need to provide the two inputs of investment return and risk-free return.

You can easily calculate this premium in the template provided.

You can download this risk premium template here – Risk Premium Excel Template

Risk Premium Formula | Calculator (with Excel Template)