Question

Calculation of the risk premium.

Answer 1

Risk Premium

A risk premium is a return on investment above the risk-free rate that an investor needs to be compensated for investing in higher-risk investments. Put simply, the more risk an investment has, the higher the return an investor needs to make it worthwhile.

It’s also known as the risk premium equation of the default risk premium and is commonly used by investors and finance students who deal with the financial markets. Risk premium is used to calculate how much a potential investor needs to be compensated for taking on extra risk when compared to a lower “risk-free” investment.

Typically, the US treasury bill (T-bill) is used as the risk-free rate in the US, but in finance theory the risk-free rate is any investment which has no risk.

Risk Premium Formula

(Risk Premium= ra​−rf​ )

• r_a = Return on asset/investment
• r_f = Risk-free return

The risk premium of an investment is calculated by subtracting the risk-free return on investment from the actual return on investment and is a useful tool for estimating expected returns on relatively risky investments when compared to a risk-free investment.

Market Risk Premium

The market’s risk premium is the average market return less the risk-free rate. For shares, the word “market” can be connoted as a whole stock index such as the S&P 500 or the Dow. The risk premium on the market may be shown as:

(Market RiskPremium=Rm​−Rf​ )

• R_m = Market return
• R_f = Risk-free return

The market risk is called systematic risk. Unsystematic risk, on the other hand, is the amount of risk associated with a particular investment and is not market-related.

The amount of risk approaches that of the market as an investor diversifies their investment portfolio. The many clichés about diversifying the investment portfolio are extracted from systemic and unsystematic uncertainty and its relationship to returns.

Risk Premium on a Stock Using CAPM

The risk premium for a particular investment using the capital asset pricing model is beta times the difference between market return and risk-free return on investment.

[ERi​=Rf​+Bi​(ERm​−Rf​)]

• ER_i = Expected return of investment
• R_f = Risk-free rate
• B_i = Beta of the investment
• (ER_m – R_f) = Market risk premium

As noted earlier, market risk premium refers to the return on the market minus the return on a risk-free investment and it’s used in CAPM to factor in the systematic risk of an investment.

Risk Premium Example

Amy is planning to invest $50,000 in order to get a large return. With the financial crisis, she is very aware of the potential risk and wants to strike an investment balance between risk and return.

She has the option to invest in risk-free investments like the US treasury bond which returns 3% a year, and also has the option to invest in a uranium stock, which is higher risk but has a potential 21% return.

Let’s calculate Amy’s risk premium:

Return on Investment=$50,000×21%=$10,500

Risk−free Return=$50,000×3%=$1,500

Risk Premium=$10,500−$1,500=$9,000

So here we see that Amy has a risk premium of $9,000. This is a rough estimate of expected returns on the risky investment into uranium. It’s important to note that this is completely dependant on the performance of the stock and Amy would need to better understand the risk factors by studying the stock at length to decide whether it’s worth investment and if it can realize the risk premium return of $9,000.

Risk Premium Conclusion

When calculating risk premium, the below points are worth bearing in mind as a quick recap of what it is, why it’s used, and how to use it:

• The risk premium is the return on an investment minus the return on a risk-free investment.
• The market’s risk premium is the average market return less the risk-free rate.
• For shares, the word “market” can be connoted as a whole stock index such as the S&P 500 or the Dow.
• The market risk is called systematic risk. Unsystematic risk, on the other hand, is the amount of risk associated with a particular investment and is not market-related.
• The risk premium for a particular investment using the capital asset pricing model is beta times the difference between market return and risk-free return on investment.