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 ```The returns on both a portfolio of common stocks and a portfolio of Treasury bills are contingent on the state of the economy, as shown below. Economic Conditions Probability Market Return Treasury Bills Recession 0.25 -8.2% 3.5% Normal 0.50 12.3 3.5 Boom 0.25 25.8 3.5 a. Calculate the expected returns on the Treasury bills and on the market. b. Calculate the expected risk premium.```
 ```Bladehulk ? 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 growth slows. 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) Where, 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. Wikipedia ?Capital Asset Pricing Model,? (Sept. 15, 2005) http://en.wikipedia.org/wiki/Capital_asset_pricing_model 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: NobelPrize.org ?THIS YEAR'S LAUREATES ARE PIONEERS IN THE THEORY OF FINANCIAL ECONOMICS AND CORPORATE FINANCE,? (Oct. 16, 1990) http://nobelprize.org/economics/laureates/1990/press.html Google search strategy: CAPM + ?market risk? Best regards, Omnivorous-GA```