Part 1
The expected return indicates the amount, either a loss or profit that investors anticipate to get from an investment which has a known rate of return. It considers the future chance that an outcome – particularly a benefit or loss would happen – and this makes it appear like forward looking since it considers the future and assesses what is likely to happen. Investors are optimistic when it comes to making profits or returns from investments hence through the best market analysis techniques, they associate a particular benefit or return with a particular probabilistic number that measures chance of occurring for such returns (Brotherson, Eades, Harris, & Higgins, 2015). For example, an expected return of 1% on a $1 million investment is $10,000 which may be speculated to be earned after six months. The main challenge associated with the expected is that, the future is always unknown and it is hard to accurately forecast what will happen in the future (risk ahead). Some exogenous factors in the market are unpredictable and this makes the expected rate of return an inefficient approach to estimate returns.
Part 2
The allocations between the market portfolio and risk-free securities can influence the levels of risk in the market through using concepts such as expected, trailing, and the required levels of market premiums (Brotherson et al. 2015). Depending with how the funds are allocated, then it is possible to identify the category in which class of risk the investment fall under. Investors can invest in risk free securities or securities with significant market risk. They use beta to assess the overall market risk – and investments with free market risk have a beta of zero. With this in mind, balancing the portfolio for either the risk-free or risky securities, the overall risk is determined by only the risk attracting securities. Supposed an investor makes 35% investments in risk free securities and 65% in risky securities, then the overall risk associated with this portfolio would be 0.65 which is the beta. Still, purchasing all risk-free securities attracts a zero risk (beta = 0) and this is a typical risk averse investor. However, investors who accommodate risky securities in their portfolio are risk tolerant – though balancing between these two types of securities can strike a balanced risk level with better outcome or returns (Bali & Zhou, 2016). Actually, risk-free securities fetch very low returns unlike the risky ones.
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Problem 1
Computing the expected return
Expected return = ∑ (Weight of the return * probability)
= ∑ [(60 * 0.1) + (30 * 0.5) + (0.40 * -23)]
= 6 + 15 – 9.2
= 11.8
In the above solution, the expected return is a summation of the individual expected return, given by multiplying the weight of the return and its respective probability, for the three economic states (Bali & Zhou, 2016).
Problem 2
Required return = Risk premium plus Risk free rate
= 4% + 7%
= 11%
Problem 3
Average annual return S&P 500 = 14.8% (market rate) and T-bill had a return of 5.6% (risk free rate)
Market premium = expected market rate – risk free rate
= 14.8% - 5.6%
= 9.20%
Problem 4
Conglomco beta = 0.32; Market return = 12%; Risk free rate = 5%
Using the CAPM model, the required return will be given as:
ER = Rf + B*(Rm – Rf)
= 5% + 0.32*[12%-5%]
= 5% + 2.24%
= 7.24%
Problem 5
Calculating the weighted beta of a portfolio
Weighted portfolio = ∑ (Beta * Weight)
Conglomco stock = 3.9 * 35%
= 1.365
Supercorp stock = 1.7 * 25%
= 0.425
Megaorg stock = 0.3 * 40%
= 0.12
Weighted portfolio beta = ∑ (0.12 + 0.425 + 1.365)
= 1.91
References
Bali, T. G., & Zhou, H. (2016). Risk, uncertainty, and expected returns. Journal of Financial and Quantitative Analysis , 51 (3), 707-735.
Brotherson, W. T., Eades, K. M., Harris, R. S., & Higgins, R. C. (2015). 'Best Practices' in Estimating the Cost of Capital: An Update.
