i Let p be the log-price of a given asset. The corresponding log-return That is defined...

 

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i Let p be the log-price of a given asset. The corresponding log-return That is defined as: THIPH-P Assume you have observations from a sample of size T. Show that the average log-return F may be computed from the log-prices at times Tand 0 only thus disregarding the rest of the observations, The average net-return Rover K periods is given by 1/K (1+R₂) -1 R= Li-I From the above equation derive the relationship between average log- return and log-returns r Question2 In the Risk Management literature there are frequent references to the square root rule 1. In relation to variances it states that Vin(K)] K-Vin] K-0² (1) where is the variance of the log-returns ry and ri(K) is the K-period aggregate return: T(K) = Ti Σ 10 For simplicity assume that the variance a of r, is constant. Clearly specify under what conditions equation (1) is correct. 2. In relation to the VaR it states that VaR(K) = √K-VaR(1) (2) where VaR(1) is the VaR of the log-returns ry and VaR(1) is the VaR of the K-period aggregate returms. Assuming the mean of r, is zero i Let p be the log-price of a given asset. The corresponding log-return That is defined as: THIPH-P Assume you have observations from a sample of size T. Show that the average log-return F may be computed from the log-prices at times Tand 0 only thus disregarding the rest of the observations, The average net-return Rover K periods is given by 1/K (1+R₂) -1 R= Li-I From the above equation derive the relationship between average log- return and log-returns r Question2 In the Risk Management literature there are frequent references to the square root rule 1. In relation to variances it states that Vin(K)] K-Vin] K-0² (1) where is the variance of the log-returns ry and ri(K) is the K-period aggregate return: T(K) = Ti Σ 10 For simplicity assume that the variance a of r, is constant. Clearly specify under what conditions equation (1) is correct. 2. In relation to the VaR it states that VaR(K) = √K-VaR(1) (2) where VaR(1) is the VaR of the log-returns ry and VaR(1) is the VaR of the K-period aggregate returms. Assuming the mean of r, is zero

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Question 1 i To show that the average logreturn can be computed from the logprices at times T and 0 only we need to demonstrate that the logreturn at time t1 denoted as rt1 can be expressed solely in ... View the full answer