Fin 421 Assignment 2-3
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Prof. Oliver Boguth FIN 421 Assignment 2 Please submit assignments (one per group) to asufi[email protected] by Monday, Oct 10th, at 6 pm. No late assignments will be accepted. If submitting an excel file, make sure you do not submit unnecessary pages of data and create a summary tab containing all answers. The cost of estimation error This question intends to show the costs investors face due to estimation error in a controlled simulation setting. We simulate returns for N = 10 identically distributed assets over T = 100 years. We will use the first T 1 = 20 years for estimation and portfolio choice(“in-sample”), and the remaining T 2 = T - T 1 years as “out-of-sample” holding (evaluation) period. All assets have a mean μ n =0.05 and standard deviation σ n =0.30, and each pairwise correla- tion is ρ n,m =0.36. The easiest way to implement this is by using a one-factor model. To do this, generate factor return F t ∼N (0.05, 0.18 2 ). The asset returns are then R n,t = F t + ε n,t , where ε n,t ∼N (0, 0.24 2 ). A. What are the optimal portfolio weights for a utility maximizing investor with risk aversion A = 5 that knows the return generating process? Compute in-sample and out-of-sample mean, standard deviation, and utility using these portfolio weights. B. Estimate means, standard deviations, and covariances, using the first T 1 observations, and find the optimal portfolio weights for above investor using “naive” portfolio choice. Compute in-sample and out-of-sample mean, standard deviation, and utility using these portfolio weights. C. Estimate factor model intercepts (“=intercept()”), betas (“=slope”), and the model implied covariance matrix using the first T 1 observations, and find the optimal portfolio weights for above investor using this factor model. Compute in-sample and out-of-sample mean, standard deviation, and utility using these portfolio weights. D. Which approach works best in sample? Which out of sample? E. Can you think of other ways to address the problems arising from estimation error? Imple- ment one idea and compare the results. Hints • Once the data are simulated, copy and “paste special → paste values” to prevent your input data from changing • The factor model covariance is a bit complicated: The diagonal cells (variances) are based on a different formula than the off-diagonals (covariances). It is probably easiest to break up the matrix into diagonal and off-diagonal.
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Transcript of Fin 421 Assignment 2-3
Prof. Oliver Boguth FIN 421
Assignment 2
Please submit assignments (one per group) to [email protected] by Monday, Oct 10th,at 6 pm. No late assignments will be accepted. If submitting an excel file, make sure you donot submit unnecessary pages of data and create a summary tab containing all answers.
The cost of estimation error
This question intends to show the costs investors face due to estimation error in a controlledsimulation setting. We simulate returns for N = 10 identically distributed assets over T = 100years. We will use the first T1 = 20 years for estimation and portfolio choice(“in-sample”), andthe remaining T2 = T − T1 years as “out-of-sample” holding (evaluation) period.
All assets have a mean µn = 0.05 and standard deviation σn = 0.30, and each pairwise correla-tion is ρn,m = 0.36. The easiest way to implement this is by using a one-factor model. To dothis, generate factor return Ft ∼ N (0.05, 0.182). The asset returns are then Rn,t = Ft + εn,t,where εn,t ∼ N (0, 0.242).
A. What are the optimal portfolio weights for a utility maximizing investor with risk aversionA = 5 that knows the return generating process? Compute in-sample and out-of-samplemean, standard deviation, and utility using these portfolio weights.
B. Estimate means, standard deviations, and covariances, using the first T1 observations, andfind the optimal portfolio weights for above investor using “naive” portfolio choice. Computein-sample and out-of-sample mean, standard deviation, and utility using these portfolioweights.
C. Estimate factor model intercepts (“=intercept()”), betas (“=slope”), and the model impliedcovariance matrix using the first T1 observations, and find the optimal portfolio weightsfor above investor using this factor model. Compute in-sample and out-of-sample mean,standard deviation, and utility using these portfolio weights.
D. Which approach works best in sample? Which out of sample?
E. Can you think of other ways to address the problems arising from estimation error? Imple-ment one idea and compare the results.
Hints
• Once the data are simulated, copy and “paste special → paste values” to prevent yourinput data from changing
• The factor model covariance is a bit complicated: The diagonal cells (variances) are basedon a different formula than the off-diagonals (covariances). It is probably easiest to breakup the matrix into diagonal and off-diagonal.
