The expected value, usually abbreviated as E(V), is the sum of each of
the three expected values multiplied by the probability.
So, E(rM) = E(recession) * P(recession) + E(normal) * P(normal) + E(boom) * P(boom)
= (0.25 * -8.2%) + (0.50 * 12.3%) + (0.25 * 25.8%)
= -2.05% + 6.15% + 6.45% = 10.55%
I?ve used the term rM, returns to market, because that is what is
typically used for the Capital Asset Pricing model (CAPM).
Your Treasury bill rate or rf (risk-free rate) is the same in all
three cases at 3.5%. In the real world, the Federal Reserve will
likely raise rates during boom times and lower them when economic
So, for (a):
rM (return on the market) = 10.55%
rf (Treasury bills) = 3.5%
CAPITAL ASSET PRICING MODEL (CAPM)
William F. Sharpe developed the CAPM during the late 1960s and it
became widely used by the mid-1970s to determine risk premiums for
market and for individual stocks. Investors in the market should
expect a higher return rM, if they?re properly diversified. Market
returns go up and down as an economy goes through recessions and boom
times but on average the market returns will be
higher than just parking money in a Treasury bill.
The MARKET risk premium is the term (rM ? rf) in the formula below:
Rc = rf + ßc(rM - rf)
Rc is the company's expected return on capital
rf is the risk-free return rate, usually a long-term U.S. Treasury bill rate
rM is the expected return on the entire market of all investments.
Most measures use a common broad index, most often the S&P500 over the
past 5 or 10 years
ßc is the company's beta, based on its covariance with the market.
?Capital Asset Pricing Model,? (Sept. 15, 2005)
Your risk premium for the stock market as a whole is 10.55% - 3.5% = 7.05%.
Thus, a diversified portfolio should give results slightly more than
triple what a Treasury bill would yield (10.55% vs. 3.5%). It doesn?t
mean that just any company will provide those additional returns ?
only that a properly diversified portfolio will. There is additional
company-related risk in the beta coefficient for each company.
Sharpe?s work on this issue won him the Nobel Prize for the work in 1990:
?THIS YEAR'S LAUREATES ARE PIONEERS IN THE THEORY OF FINANCIAL
ECONOMICS AND CORPORATE FINANCE,? (Oct. 16, 1990)
Google search strategy:
CAPM + ?market risk?