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4 b2 expected return b4 efficient frontier p a

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Unformatted text preview: ond ORP (such as B2) that are formed by combining risk free borrowing with the ORP . 4 B2 Expected return B4 efficient frontier P – A randomly selected portfolio rf ORP – Optimal risky portfolio corresponding to the borrowing rate Standard deviation of returns F. The current level of utility is 5.1238 (5.4961 – 0.005×4×4.31472). To determine if the current allocation between rf and the ORP is optimal, use the solver function to check if another balanced portfolio with a larger utility can be formed, i.e., maximise the utility of the balanced portfolio by changing the weight allocated to the ORP subject to the constraint the weight allocated to the ORP is greater than or equal to 0. The optimal allocation is 59.96% in the ORP and 40.04% in risk free lending. This OBP offers a utility of 5.1652. Portfolio Composition ORP BP OBP 0.9000 0.5996 rf 0.1000 0.4004 E(ROBP) 5.4961% 5.3305% σOBP 4.3147% 2.8744% A 4.00 4.00 Utility 5.1238 5.1652 G. The process involved in determining the ORP is separate from and independent of the process involved in determining the OBP. While the choice of ORP is based on the reward to variability ratio, the choice of OBP is based on the utility derived from the risk return combination of a portfolio. The degree of risk aversion affects the choice of OBP, but not ORP. These outcomes are known as the separation theorem H. i) The reward to variability ratio of the two portfolios are first computed below: For EP1, RTVR = (10% - 4%) / 4% = 1.5 (no unit) For EP2, RTVR = (16% - 4%) / 20% = 0.6 EP1 is preferred as it has the larger reward to variability ratio. ii) The RTVR of the other portfolio must equate to 1.5. Let the expected return of the other portfolio be ?, (? – 4%) / 20% = 1.5 ? = 34% 5 iii)The investor should form a balanced portfolio consisting of EP1 and rf with the following composition where y is the proportion of funds in EP1: y × 0.1 + (1 - y) 0.04 = 0.34 ⇒ y = 5 OR y × 0.04 = 0.20 ⇒y=5 (The first (second) equation computes the expected return (risk) of the balanced portfolio.) With an initial wealth of $100, the investor should borrow $400 (since 1 - y = 4) at the risk free rate and invest $500 in EP1. 6 7...
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