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Harman [31]
3 years ago
8

An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 0.05 and she put

s 30% in a Treasury bill that pays 5%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively.
Business
1 answer:
Mazyrski [523]3 years ago
6 0

Answer:

The portfolio's expected return is 12% and the standard deviation of the portfolio is 15.65%.

Explanation:

The expected rate of return of the portfolio is the weighted average of the individual stock returns that form up the portfolio. The formula for a two stock portfolio return is,

Portfolio return = wA * rA + wB * rB

Where,

  • w represents weight of the stocks in the portfolio
  • r represents the return of the stocks in the portfolio

Portfolio return = 0.7 * 0.15  +  0.3 * 0.05  =  0.12 or 12%

The portfolio which consists of a risky and a risk free asset has a standard deviation equal to the weight of the risky asset multiplied by its standard deviation. The risk free asset has no standard deviation. Thus, the formula for a portfolio standard deviation for such a portfolio is,

Standard deviation = weight of risky asset * standard deviation of risky asset

Standard deviation of portfolio = 0.7 * √0.05

Where standard deviation is the square root of variance.

Standard deviation of portfolio = 0.1565 or 15.65%

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What is present value?
The present value of a prospective sum of money or cash flow stream given a specified return rate is known as its present value (PV). The present value of future cash flows is reduced by the discount rate, and the higher coupon rate, the lower the present value of future cash flows. The key to correctly valuing future cash flows, whether they are earnings or debt obligations, is determining the appropriate discount rate. The concept of present value states that a quantity of funds today is worth greater than the same amount in the long term. In other words, money gained in the long term is not as valuable as money received today.

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To learn more about present value
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