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You invest $2,100 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 20% and a Treasury bill with a rate of return of 7%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 13%.

User ALOK KUMAR
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2 Answers

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Final answer:

The question deals with the calculation of the proportion of funds to invest in a risky asset to achieve a desired portfolio standard deviation. It involves investment and portfolio management concepts. Without the specific formula for the risk calculation in this context, an exact answer cannot be provided.

Step-by-step explanation:

The student asks what portion of their complete portfolio should be invested in a risky asset to achieve a desired standard deviation of 13% for the overall portfolio. This is a problem involving the allocation of funds between risky and risk-free assets to achieve a certain level of portfolio risk, primarily related to investment and portfolio management. To solve this, one would typically use the concept of combining a risk-free asset, in this case, Treasury bills, with a risky asset, to find the proportion invested in the risky asset that results in the desired risk level.

However, without the exact formula for the risk of a complete portfolio based on investment proportions, we're not able to compute the answer to the question directly. It's important to note that in the finance world, higher risk is associated with the potential for higher returns as compensation for the increased uncertainty. This is why stocks historically have offered higher returns than bonds, which in turn offer higher returns than savings accounts.

User Whakkee
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Answer: 65%

Step-by-step explanation:

The formula that's used for the calculation of the portfolio's standard deviation will be:

(Standard deviation of portfolio)² = (Weight of asset)² × (Standard deviation of asset)²

(Weight of asset)² = (0.13)²/(0.2)² = 0.0169 / 0.04

= 0.4225

Weight of asset = ✓0.4225

Weight of asset = 0.65

Weight of asset = 65%

Therefore, 65% of the portfolio should be invested.

User LikerRr
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