efficient%20frontier%20DQ

efficient%20frontier%20DQ - Session 6: Locating the...

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Unformatted text preview: Session 6: Locating the Efficient Frontier A. S1 P8 P9 S2 L1 L2 E(RP) 0.0000 0.0000 0.1000 0.0000 0.3000 0.3000 0.6000 0.7000 5.5660% 5.5980% σP 5.0394% 5.3116% σP B. S1 S2 L1 L2 E(RP) … … … … … … … EP8 EP9 0.0939 0.0030 0.0000 0.0000 0.0000 0.0000 0.9061 0.9970 5.5790% 5.6090% 5.0394% 5.3115% C. Investing in highly correlated assets is like putting money in the same asset. Thus there is little diversification benefit from investing in these assets. Investors are better off diversifying their investments into assets that are not highly correlated. From the following table that shows the correlation coefficients among the four bonds, while bonds in the same maturity group are highly correlated, bonds in different maturity groups are not. Therefore, there is no need to invest in each and every short term bond and each and every long term bonds, just one from each maturity category is sufficient. S1 S1 S2 L1 L2 S2 1.00 0.93 0.80 0.75 L1 1.00 0.74 0.70 L2 1.00 0.99 1.00 D. A ORPLRA ORPMRA Utility S1 S2 L1 L2 E(RP) σP 2.50 8.00 5.2642 4.9110 0.2202 0.9025 0.0000 0.0000 0.0000 0.0000 0.7798 0.0975 5.5373% 5.3122% 4.6743% 3.1669% E. Table Ia - Risk Return Combination of 9 Efficient Portfolios - with Short Selling S1 S2 L1 L2 E(RP) σP EP1 1.1217 -0.2151 -2.3911 2.4844 5.4043% 3.1550% EP2 1.0507 -0.1980 -2.4514 2.5988 5.4247% 3.2897% EP3 0.9986 -0.2008 -2.5034 2.7057 5.4449% 3.4318% EP4 0.8950 -0.1657 -2.5696 2.8403 5.4704% 3.6228% EP5 0.7690 -0.1754 -2.7136 3.1200 5.5209% 4.0292% EP6 0.5337 -0.0899 -2.8512 3.4073 5.5767% 4.5129% EP7 0.5191 -0.1511 -2.9161 3.5481 5.6037% 4.7572% EP8 0.3449 -0.0560 -3.0033 3.7145 5.6342% 5.0395% EP9 0.3343 -0.1256 -3.0816 3.8729 5.6631% 5.3117% Table Ka: A Summary of the Optimal Risky Portfolios - with Short Selling ORPLRA ORPMRA A 2.50 8.00 Utility 5.3221 5.0258 S1 0.5816 1.3261 S2 -0.1272 -0.2470 L1 -2.8828 -2.2054 L2 3.4285 2.1263 E(RP) 5.5741% 5.3396% σP 4.4897% 2.8012% 1 F. 5.7000% 5.6500% Expected return 5.6000% 5.5500% 5.5000% No short selling 5.4500% With short selling 5.4000% ORP(MRA ) - no short selling ORP(LRA ) - no short selling 5.3500% ORP(MRA ) - w ith short selling 5.3000% ORP(LRA ) - w ith short selling 5 .2500% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% 5.50% Standard deviation The efficient frontier is higher up with short selling than without implying that: there are more attainable portfolios with better risk return combinations and investors can gain a higher level of utility. For example, comparing the ORP with short selling to the ORP without short selling selected by the more risk averse, the former has higher expected return and lower risk. The same is true to the two ORPs corresponding to the less risk averse. G. The statement is not true. Although an asset may be very risky, as long as it does not correlate perfectly with other assets, one may include the very risky asset in a portfolio so as to improve a better risk-return combination. While the level of expected return will increase proportionately (to the weight allocated to the very risky asset), there will be a less than proportionate increase in the level of risk. Referring to the bond portfolio, although the long term bond is the most risky among the four, it is included in the efficient portfolio. H. 2 2 2 2 2 2 w12 σ 12 + w2 σ 2 + w3 σ 32 + w4 σ 4 + w5 σ 52 + 2 w1 w2 σ 1, 2 + 2 w1 w3 σ 1,3 + 2 w1 w4 σ 1, 4 + 2 w1 w5 σ 1,5 + σ P = 2w2 w3 σ 2,3 + 2w2 w4 σ 2, 4 + 2w2 w5 σ 2,5 + 2 w3 w4 σ 3, 4 + 2w3 w5 σ 3,5 + 2 w4 w5 σ 4,5 There are all together 5 variance terms and 10 unique covariance terms. 2 ...
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This note was uploaded on 10/29/2010 for the course FINS 2624 taught by Professor Hneryyip during the Three '10 term at University of New South Wales.

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