Consider two assets. Suppose that the return on asset 1 has expected value 0.02 and standard...

Consider two assets. Suppose that the return on asset 1 has expected value 0.02 and standard deviation 0.05 and suppose that the return on asset 2 has expected value 0.04 and standard deviation 0.06.

Consider an equally weighted portfolio in which each asset receives weight 1/2 and let Rp denote the return on the portfolio.

Find the expected value of Rp and the variance of Rp as functions of ρ12, the correlation of the returns on the two assets.

Please use RStudio

Solutions

Expert Solution

Stock	Return	SD	Weigh
A	0.02	5%	0.5
B	0.04	6%	0.5

Expected Return = w₁ x r₁ + w₂ x r₂

= 0.5 x 0.02 + 0.5 x 0.04

= 0.01 + 0.02

= 0.03 or 3%

Variance as a function of P₁₂

Variance = w₁² σ²_{1 +} w₂² σ₂² + 2 w₁ w₂ σ₁ σ₂ P₁₂

σ_p² = (0.5)²(5)² + (0.5)²(6)² + 2 x 0.5 x 0.5 x 6 x 5 x P₁₂

σ_p² = 6.25 + 9 + 15 P₁₂

σ_p² = 15.25 + 15 P₁₂ Variance as a function of P₁₂ (Required Equation)

jeff jeffy answered 2 years ago

Next > < Previous

Related Solutions

Consider two assets. Suppose that the return on asset 1 has expected value 0.06 and standard...

Consider two assets. Suppose that the return on asset 1 has expected value 0.06 and standard deviation 0.15 and suppose that the return on asset 2 has expected value 0.03 and standard deviation 0.08. Suppose that the asset returns have correlation 0.35. Consider a portfolio placing weight ω on asset 1 and weight 1-ω on asset 2. Let Rp denote the return on the portfolio. Find the mean, variance, and standard deviation of Rp as a function of ω. Display...

Consider the following two assets: Asset A’s expected return is 15% and return standard deviation is...

Consider the following two assets: Asset A’s expected return is 15% and return standard deviation is 20%. Asset B’s expected return is 10% and return standard deviation is 15%. The correlation between assets A and B is 0.5. (a) w1=0.75, w2=.50, find out expected returns and SD/VARIANCE (b) Instead of a correlation of 0.5 between assets A and B, consider a correlation of - 0.5 and re-compute the above.

Consider a set of risky assets that has the following expected return and standard deviation: Asset...

Consider a set of risky assets that has the following expected return and standard deviation: Asset Expected Return E(r) Standard Deviation 1 0.12 0.3 2 0.15 0.5 3 0.21 0.16 4 0.24 0.21 If your utility function is as described in the book/lecture with a coefficient of risk aversion of 4.0 , then what is the second-lowest utility you can obtain from an investment in one (and only one) of these assets? Please calculate utility using returns expressed in decimal form...

There are 2 assets. Asset 1: Expected return 7.5%, standard deviation 9% Asset 2: Expected return...

There are 2 assets. Asset 1: Expected return 7.5%, standard deviation 9% Asset 2: Expected return 11%, standard deviation 12%, correlation with asset 1 is 0.4 You hold 30% of your portfolio in asset 1 and 70% in asset 2. a) (1 point) What is the expected return of your portfolio? b) (1 point) What is the covariance between assets 1 and 2? c) (1 point) What is the standard deviation of your portfolio?

suppose asset a has an expected return of 10% and a standard deviation of 20% asset...

suppose asset a has an expected return of 10% and a standard deviation of 20% asset b has an expected return of 16% and a standard deviation of 40%.if the correlation between a and b is 0.6,what are the expected return and standard deviation for a prtifolio comprised of 40% asset a

Narrative Two Given the following information about two assets: Expected Return of Asset 1 12.00% Standard...

Narrative Two Given the following information about two assets: Expected Return of Asset 1 12.00% Standard Deviation of Asset 1 8.00% Expected Return of Asset 2 16.00% Standard Deviation of Asset 2 15.00% 1. Calculate the minimum standard deviation of a two-asset portfolio consisting of these two assets when the covariance between Asset 1's return and Asset 2's return is -0.009. 2.Calculate the standard deviation of a two-asset portfolio consisting of these two assets when w1 = 0.75 and the...

expected return and standard deviation. stateecon, probability, asset A, asset B, Asset C boom. 0.34. 0.02. &nbs

expected return and standard deviation. stateecon, probability, asset A, asset B, Asset C boom. 0.34. 0.02. 0.22. 0.34 normal. 0.52. 0.02. 0.05. 0.18 recession. 0.14. 0.02. -0.01. -0.25 A) what is the expected return of each asset? B) what is the variance of each Asset? C) what is the standard deviation of each asset?

Asset A has an expected return of 15% and standard deviation of 20%. Asset B has an expected return of 20% and standard deviation of 15%.

1. Asset A has an expected return of 15% and standard deviation of 20%. Asset B has an expected return of 20% and standard deviation of 15%. The riskfree rate is 5%. A risk-averse investor would prefer a portfolio using the risk-free asset and _______. A) asset A B) asset B C) no risky asset D) cannot tell from data provided2. The Sharpe-ratio is useful for A) borrowing capital for investing B) investing available capital C) correctly...

Suppose that you are given the following information about an asset: Asset Expected Return Expected Standard...

Suppose that you are given the following information about an asset: Asset Expected Return Expected Standard Deviation X .1 .04 Y .15 .08 Z .2 .09 (10 points) If you invested 50% of your portfolio in X and 50% in Y, what would be the expected return and standard deviation of the portfolio if the correlation coefficient between X and Y is .5? (10 points) If you invested 50% of your portfolio in X and 50% in Z, what would...

Asset 1 has an expected return of 10% and a standard deviation of 20%. Asset 2...

Asset 1 has an expected return of 10% and a standard deviation of 20%. Asset 2 has an expected return of 15% and a standard deviation of 30%. The correlation between the two assets is less than 1.0 i.e., they are not perfectly correlated. You form a portfolio by investing half of your money in asset 1 and half in asset 2. Which of the following best describes the expected return and standard deviation of your portfolio? The expected return...

Subjects