CAPM
&
The Country Risk Premium
1
• To reflect the increased risk associated with investing
in a developing country, a country risk premium is
added to the market risk premium when using the
CAPM.
Problem
Consider the following annual returns of the stock BMB
(american company) and of the market index (S&P 500) :
Year
RBMB
S&P500
Rf (USA)
1
11%
15%
5%
2
6%
10%
5.3%
3
12%
14%
5%
4
20%
18%
3.5%
5
10%
12%
4%
6
15%
16%
4.5%
Instructions:
1. Determine RRRBMB using the CAPM and assuming a current Rf (risk free rate in
the U.S (10 years T-yield)) of 4.2%
Solution:
RRRBMB = Rf + βBMB(RRRM-Rf)
With RRRM = RRRS&P500
βBMB = CovBMB,S&P500/ V(S&P500) = 1.58
Expected Market risk premium = average (RS&P500 – Rf) =
9.62%
RRRBMB = 4.2% + (1.58 * 9.62%) = 19.39%
NB: Beta is a measure of the volatility, or systematic risk,
of a security or a portfolio in comparison to the market
as a whole. Beta represents the tendency of a security's
returns to respond to swings in the market.
-A beta of 1 indicates that the security's price moves
with the market.
-A beta of less than 1 means that the security is
theoretically less volatile than the market.
-A beta of greater than 1 indicates that the security's
price is theoretically more volatile than the market.
Problem
Consider the following annual returns of the stock CMC
(Tunisian company) and of the market index (S&P 500) :
Year
RCMC
S&P500
Rf (USA)
1
11%
15%
5%
2
6%
10%
5.3%
3
12%
14%
5%
4
20%
18%
3.5%
5
10%
12%
4%
6
15%
16%
4.5%
Instructions:
Determine RRRCMC using the CAPM and assuming a current Rf of 4.2% (from an
american investor viewpoint)
• From an american investor viewpoint, we have to
add a Country Risk Premium (CRP)
CRP: Definition:
• A country risk premium (CRP) is the additional risk
associated with investing in an international company
rather than the domestic market.
• Macroeconomic
factors such as political instability,
volatile exchange rates and economic turmoil causes
investors to be wary of overseas investment opportunities
and thus require a premium for investing.
• The country risk premium (CRP) is higher for developing
markets than for developed nations.
• Within the american market (« i » is an american
stock, and the analysis is made from an american
investor viewpoint) :
Risk i = βi RiskM
• Risk premium i = βi Risk premiumM
• RRRi – Rf = βi (RRRM – Rf)
• RRRi = Rf + βi (RRRM – Rf)
• How if « i » is a Tunisian stock, and the analysis is
made from an american investor viewpoint :
American market
Risk i = βi (Risk M + additional country risk for Tunisia)
• Risk premium i = βi x (Risk premium on M + additional
risk premium for moving from investing in USA to
investing in Tunisia)
• RRRi – Rf = βi (RRRM – Rf + CRP)
• RRRi = Rf + βi (RRRM – Rf + CRP)
The revised CAPM equation is stated as:
RRRi = Rf + βi [RRRS&P500– Rf + CRP]
American
market RP
Where
CRP : country risk premium (Marginal: additional)
Rf: risk free rate in U.S
RRRS&P500: RRR on the american market (S&P500).
• How to find CRP?
• The
general risk of the developing country is
reflected in its sovereign yield spread.
• This
is the difference in yields between the
developing
country's
government
bonds
(denominated in the developed market's currency)
and Treasury bonds of a similar maturity.
Example:
•
Tunisian
U.S.
dollar-denominated
government bond yield = 7.8%.
• 10-year U.S. Treasury bond yield = 4.8%.
10-year
Sovereign yield spread for Tunisia = 7.8% - 4.8% = 3%
3% is the additional risk premium on the bond market. However
we are interested in the additional risk premium on the stock
market.
Suppose :
-Annualized standard deviation of Tunisian stock index = 25%.
-Annualized standard deviation of Tunisian U.S. dollardenominated 10-year government bond = 12.5%.
Thus, Tunisian stock market is 2 times more volatile (more risky)
than its sovereign bond market.
Therefore, the risk premium on stock market should be 2 x 3% =
6%
CRP = 6%
Solution:
RRRCMC = Rf + βCMC(RRRM-Rf + CRP)
With RRRM) = RRRS&P500
βCMC = CovCMC,S&P500/ V(S&P500) = 1.58
Expected Market risk premium = average (RS&P500 – Rf) =
9.62%
RRRCMC = 4.2% + [1.58 * (9.62% + 6%)] = 28.88 %
Example: Country risk premium
Robert Smith, an analyst with Omni Corporation, is estimating a country risk
premium to include in his estimate of the cost of equity for a project Omni
is starting in Venezuela. Smith has compiled the following information for his
analysis:
• Venezuelan U.S. dollar-denominated 10-year government bond yield =
8.6%.
• 10-year U.S. Treasury bond yield = 4.8%.
• Annualized standard deviation of Venezuelan stock index = 32%.
• Annualized standard deviation of Venezuelan U.S. dollar-denominated 10year government bond = 22%.
• Project beta = 1.25.
• Expected american market return (RRRM) = 10.4%.
• Risk-free rate = 4.2%.
Calculate the country risk premium and the cost of equity for Omni's
Venezuelan project.
• Problem 27 page 38
Problem
Consider the following annual returns of the stock DMD
(Indian company) and of the market index (S&P 500) :
Year
RDMD
S&P500
Rf (USA)
1
12%
15%
5%
2
18%
10%
5.3%
3
6%
14%
5%
4
20%
18%
3.5%
Instructions:
Determine RRRDMD using the CAPM and assuming a current Rf of 4.2% (from an
american investor viewpoint)
Additional information :
- Indian U.S. dollar-denominated 10-year government
bond yield = 9.6%.
- 10-year U.S. Treasury bond yield = 4.8%.
• Annualized standard deviation of Indian stock index
= 30%.
• Annualized standard deviation of Indian U.S. dollardenominated 10-year government bond = 20%.