1-a) As Jerry wants to invest in the lowest risk portfolio, his main goal is to lower the risk irrespective of returns so he should go with an asset with the lowest standard deviation. as standard deviation is the measure of risk here so Safe asset is the one with the lowest risk of 12%. so he should go with Safe Assets.
1-b) Staurt can earn 25% of returns just by investing in high-end asset. but while earning 25% returns he wants to minimize his risk.
So we need to combine different - different assets
Let's make a portfolio of risky and balances asset portfolio:
let say Stuart invets X in Risky asset, and 1-X in balance portfolio
So, 30*X+15*(1-X) = 25
so, X= 1/3 and 1-X =2/3
here, 1 = Standard deviation of risky assets
2 = Standard deviation of balance asset
as there is no correlation between assets so correlation =0
and w1 and w2 are the weights of risky asset and balance asset
The risk at the portfolio level can be calculated as (portfolio)^2 =w1^2 1^2+w2^22^2
(portfolio)^2 = (2/3)^2 * (40%)^2 + (1/3)^2 * (20%)^2
(Portfolio) = 27.48%
so it is better than high-end portfolio alone.
so Stuart should invest 1/3 in balance portfolio and 2/3 in the risky asset.
1- C) Same as above calculate the portfolio weight of high end and low end asset.
Let W1 = weight of balance asset. W2 = weight of safe asset
1 = Standard deviation of high-end asset 2 = Standard deviation of low-end asset
So to calculate the weight of these two assets:
W1*return on high end asset + W2* return on low end asset = required return
W1*25%+ 10%* (1-W1) = 15%
W1 = 1/3 W2 = 2/3
(portfolio)^2 =W1^2 * 1^2+W2^2 * 2^2
(portfolio)^2 = (1/3)^2* (30%)^2 + (2/3)^2 * (15%)^2
(portfolio) = 14.14%
so Dave should invest 1/3 and 2/3 in high end and low end asset.
1-D)
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