a portfolio risk identified as the weighted average of the individual stock's standard deviation the portfolios risk is generally
Added by Janet S.
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Instead, it takes into account the correlation between the returns of the stocks in the portfolio. Show more…
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true or false the risk of a portfolio is generally not equal to the weighted average standard deviatin of expected return of each stock in the portfolio
Yujie W.
When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio, A. the portfolio standard deviation is always equal to the securities' covariance. B. the portfolio standard deviation is less than the weighted average of the individual security standard deviations. C. None of the options D. the portfolio standard deviation is greater than the weighted average of the individual security standard deviations . E. the portfolio standard deviation is equal to the weighted average of the individual security standard deviations.
Jennifer S.
Value-at-risk (VaR) of a portfolio investment is a statistic that measures the level of financial risk within the portfolio over a specific time period. Consider an initial investment of AUDW₀ in a portfolio of two assets: Amazon (A) and Boeing (B). The weights attached to A and B are given by wₐ and w₂. Further, assets A and B have expected returns denoted by μₐ and μ₂ and variances given by σₐ² and σ₂² respectively. For the portfolio simple return, Rₑ, we assume that Rₑ ∼ N(μₑ, σₑ²), where μₑ and σₑ² are the expected return and variance of this portfolio. The a × 100% portfolio value-at-risk is given by VaRₒ,ₐ = qₑᴿᴾ W₀, where a ∈ (0,1) and qₑᴿᴾ is the a quantile of the distribution of Rₑ. This is defined as qₑᴿᴾ = μₑ + qₐᶠ σₑ, where qₐᶠ is the a quantile of the standard normal distribution. 1. Show analytically whether, in general, the portfolio VaR is a weighted average of the individual asset VaRs, where the weights are given by wₐ and w₂. (6 pts) 2. Assume that the correlation coefficient between assets A and B is equal to unity, i.e. ρᴀᴂ = 1. Do you reach the same conclusion as in Q2.1? Demonstrate your steps in arriving at your answer. Do you think that it is a good idea to approximate the portfolio VaR by the weighted average of the individual asset VaRs? Justify your answer. (6 pts) 3. Consider an initial investment of W₀ = AUD100,000, and an equally weighted portfolio P comprising of assets A and B. Verify your findings in Q2.1 and Q2.2 using 5% VaRs on A, B and P as well as the information in Table 2 below, when (a) ρᴀᴂ = 0.26 and (b) ρᴀᴂ = 1.00 (note that q₀₀.₅ᶠ = -1.645): Table 2 μₐ: 0.212, μ₂: 0.156, σₐ²: 0.0238, σ₂²: 0.0187
Sri K.
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