What is the Portfolio Beta?

Risk and Return. Understanding portfolio and beta?

• Conrad holds a $20,000 portfolio that consists of four stocks. His investment in each stock, as well as each stock's beta, is shown below: Stock: Aramis Airlines Investment: $3,000 Beta: 0.7 Standard Deviation: 30% Stock: Barrington Inc. Investment: $8,000 Beta: 1.8 Standard Deviation: 52% Stock: Carrow & Co. Investment: $5,000 Beta: 1.1 Standard Deviation: 38% Stock: Dartan Enterprise Investment: $4,000 Beta: 0.4 Standard Deviation: 33% 1. Which of these stocks has the least amount of total risk? 2. Which of these stocks contributes the least risk to the portfolio? 3. If the risk-free rate is 5% and the market risk premium is 6%, what is the portfolio's beta and required return? 4. Suppose an analyst believe that the expected return on Conrad's new portfolio is actually 14.80%. Does this analyst think the portfolio is undervalued, overvalued, or fairly valued? Any help and advice you can give me is very much appreciated!!!!

• Answer:

  1. on a stand alone basis, stock Aramis has the least amount of risk because it has the lowest standard deviation (of returns) 2. as part of a portfolio, stock Dartan contributes the least risk because it has the lowest (weighted) Beta. 3. to calc this...need the weighted Beta of the 4 stocks...total invested = $20k stock A: weight = 3k/20k = 0.15 times its beta of 0.7 = 0.105 stock B: weight = 8k/20k = 0.40 * 1.8 = 0.72 stock C: 5k/20k = 0.25 * 1.1 = 0.275 stock D: 4k/20k = 0.20 * 0.4 = 0.08 Portfolio Beta = 0.105 + 0.72 + 0.275 + 0.08 = 1.18 [CAPM uses Beta as a measure of risk for expected return] Expected (or "required")Return E(Rport) per CAPM = RFR + Beta(Rmarket - RFR) ...(Rmarket - RFR) = market risk premium E(Rport) = 0.05 + 1.18(0.06) E(Rport) = 0.1208 or 12.08% 4. if CAPM shows the portfolio at a 12.8% return (in other words, the portfolio "should" plot ON the SML at 12.8%), but Conrad believes the expected return is 14.8% (i.e. the portfolio is plotting ABOVE the SML), then Conrad would think the portfolio is UNDERpriced. ... as a general rule... if CAPM rate > expected return, asset plots below the SML and the stock is overpriced if CAPM rate< expected return, asset plots above the SML and the stock is underpriced Hope this helps...