Country risk premium (country spread) is the incremental required return which results from the increased risk inherent in an investment in a foreign (developing) country. It is added to the required rate of return in a developed market to arrive at appropriate required return for an investment in an emerging market.

Investing in an emerging market is typically riskier than investing in a developed market. The increased risk can come from a range of factors including unstable political environment, poor governance and regulatory environment, non-independent policy making, etc.

Since it is generally accepted that the country risk is non-diversifiable, a country risk premium must be added to the sum of the risk-free rate and the (developed market) equity risk premium.

## Formula

There are two principal methods to calculate country risk premia: (a) the sovereign yield method and (b) the equity risk premium method.

## Sovereign yield method

The sovereign yield method (also called bond yield spread method) measures the country risk premium as the difference between the yield on emerging country government bonds and the yield on same-currency developed country government bonds of the same maturity.

$$\text{CRP}\ =\ \text{Y} _ \text{F}-\text{Y} _ \text{D}$$

Where,
CRP is the country risk premium,
YF is the yield on emerging country government bonds, and
YD is the yield on developed country government bonds.

The currency of the bonds and their yield to maturity must be same to arrive at an accurate estimate of CRP.

### Sovereign yield adjusted for equity/debt volatility

Some practitioners argue that the differential yield must be adjusted by the ratio of volatility of the emerging country equity market and volatility of its sovereign bond market as follows:

$$\text{CRP}\ =\ (\text{Y} _ \text{F}-\text{Y} _ \text{D})\times\frac{\sigma _ \text{E}}{\sigma _ \text{G}}$$

Where σE is the standard deviation of the equity market returns and σG is the standard deviation of the government bonds yield.

The equity risk premium method compares the market risk premium (MRP) of the emerging market with the market risk premium of the developed market.

## Application in CAPM

There are three approaches that can be adopted in adjusting the development market required rate of return for the country risk premium using the capital asset pricing model.

The first approach assumes that exposure of each company to the country risk premium is the same as its exposure to systemic risk. Hence, it involves multiplication of the sum of the market risk premium and the country risk premium with the relevant beta coefficient to arrive at the appropriate equity risk premium for a company.

$$\text{r}=\text{r} _ \text{f}+\beta\times(\text{r} _ \text{m}-\text{r} _ \text{f}+\text{CRP})$$

The second approach assumes that all companies are equally affected by the country risk premium. Hence, it adds country risk premium to the developed market required return worked out using CAPM.

$$\text{r}=\text{r} _ \text{f}+\beta\times(\text{r} _ \text{m}-\text{r} _ \text{f})+\text{CRP}$$

The third approach involves multiplying the country risk premium with lambda, a measure of sensitivity of each investment to country risk.

$$\text{r}=\text{r} _ \text{f}+\beta\times(\text{r} _ \text{m}-\text{r} _ \text{f})+\lambda\times \text{CRP}$$

Aswath Damodaram of NYU Stern School of Business publishes estimates for country risk premium which can be accessed here.

## Example

You are an analyst working at a major US-based oil and gas company which is considering setting up an oil refinery in Pakistan. Work out the appropriate discount rate for your investment in Pakistan using the following data:

• Risk free rate in US: 3%
• Market risk premium in US: 5%
• Investment beta: 0.8
• Yield on 10-year US Treasury bonds: 4%
• Yield on 10-year US-denominated bonds of Government of Pakistan: 6.8%
• Ratio of volatility of Pakistan Stock Exchange to volatility of Pakistan USD bonds: 1.5

First, you need to measure the default spread between US Treasury bonds and USD-denominated Pakistan bonds, which is 2.8% (6.8% minus 4%). Next, you must adjust them for the difference between volatility of equity and Government bond markets.

$${\rm \text{CRP}} _ {\text{PAK}}\ =\ (\text{6.8%}-\text{4%})\times\text{1.5}=\text{5.6%}$$

You must consider how much your investment is exposed to this country risk. Even though your beta is lower than the market, let’s assume your investment’s country risk exposure is the same as the general market i.e. at a factor of 1. Your expected rate of return using CAPM must be 12.6%:

$$\text{r}=\text{3%}+\text{0.8}\times\text{5%}+\text{5.6%}=\text{12.6%}$$