8. You have a portfolio with three assets. The forecasted inputs are showed in following table....
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8. You have a portfolio with three assets. The forecasted inputs are showed in following table. Calculate expected marginal contribution to total risk (MCTR) and absolute contribution to total risk (ACTR) of each asset. Mean Portfolio Covariance Matrix Weight Asset 1 Asset 2 Asset 3 Asset 1 8% 25% 0.00860 0.00823 0.00071 Asset 2 10% 40% 0.00823 0.00972 -0.00313 Asset 3 6% 35% 0.00071 -0.00313 0.03987 = 2w0 +2 awi ; j=1,ji - Risk budgeting total risk decomposition Marginal contribution to total risk (MCTR), changes of volatility with a small change of asset position N N w; ;; = 2 cov | R, W; R + w; Rj j#i _ 2p awi awi = = 2cov(Ri, Rp) and cov(Ri, Rp) _ (w)i = MCTR = = = where i - asset i beta to portfolio from Rit = i + i Rpt + it and i the correlation between asset i and portfolio; (w); - the 7th number in w Absolute contribution to total risk (ACTR) ACTR = wiMCT Ri wi COV (Ri,Rp) = = 0% Pi i with Pi 8. You have a portfolio with three assets. The forecasted inputs are showed in following table. Calculate expected marginal contribution to total risk (MCTR) and absolute contribution to total risk (ACTR) of each asset. Mean Portfolio Covariance Matrix Weight Asset 1 Asset 2 Asset 3 Asset 1 8% 25% 0.00860 0.00823 0.00071 Asset 2 10% 40% 0.00823 0.00972 -0.00313 Asset 3 6% 35% 0.00071 -0.00313 0.03987 = 2w0 +2 awi ; j=1,ji - Risk budgeting total risk decomposition Marginal contribution to total risk (MCTR), changes of volatility with a small change of asset position N N w; ;; = 2 cov | R, W; R + w; Rj j#i _ 2p awi awi = = 2cov(Ri, Rp) and cov(Ri, Rp) _ (w)i = MCTR = = = where i - asset i beta to portfolio from Rit = i + i Rpt + it and i the correlation between asset i and portfolio; (w); - the 7th number in w Absolute contribution to total risk (ACTR) ACTR = wiMCT Ri wi COV (Ri,Rp) = = 0% Pi i with Pi
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