Module4_PortMgmt_Lecture

Module4_PortMgmt_Lecture - Course Outline I Index Models...

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Unformatted text preview: Course Outline: I Index Models, portfolio hedging and Value at Risk Computation of a Hedge Using the above Variance formula we have: Suppose we have a portfolio with a mean μ p variance σ p 2 . We want to hedge this portfolio using the Spiders. How much do we need to invest in the Spider per a dollar in vested in the portfolio. Thus our position in the portfolio is $1. Let our position in the Spiders be X H . The return of our hedged portfolio is r H = 1 * r p + X H * r m The lowest value for σ H 2 is achieved for X H = - β . and the lowes possible variance is ρ σ σ σ σ σ 2 2 2 2 2 2 B B A A B B A A P X X X X + + = ρ σ σ σ σ σ * 1 * 2 1 2 2 2 2 2 m H p m H p H X X + + = ] * 2 [ 2 2 2 2 H m p H m p H X X ρ σ σ σ σ σ + + = ] * 2 [ 2 2 2 2 H H m p H X X β σ σ σ + + = ]- ) * 2 [( 2 2 2 2 2 2 β β β σ σ σ + + + = H H m p H X X ] ) * 2 [(- 2 2 2 2 2 2 2 β β σ σ β σ σ + + + = H H m m p H X X ] ) [(- 2 2 2 2 2 2 β σ σ β σ σ + + = H m m p H X 2 2 2 2- m p H σ β σ σ = FSTEX (VaR) Hedged vs. SPY Mean-0.132%-0.132% Std 2.608% 4.021% ρ 0.81 β 1.25 Portfolio position α 0.033% $1.00 $1,000,000.00 Systematic Risk 0.001062 UnSystematic Risk 0.000555 1% VaR 0.023565 Unhedged-0.0948686 $(94,868.60) Hedged-0.054491 $(54,491.00) Price Returns Date SPY FSTEX SPY FSTEX 1/2/2008 141.52 44.56-0.04% 0.65% 1/3/2008 141.46 44.85-2.45%-2.52% 1/4/2008 137.99 43.72-0.09%-0.96% 1/7/2008 137.87 43.3-1.61%-1.36% 1/8/2008 135.65 42.71 1.05% 1.87% 1/9/2008 137.07 43.51 0.66%-0.62% 1/10/2008 137.97 43.24-0.80%-0.93% 1/11/2008 136.86 42.84 0.80% 2.05% 1/14/2008 137.96 43.72-2.20%-3.84% 1/15/2008 134.92 42.04-0.86%-3.31% 1/16/2008 133.76 40.65-2.59%-3.79% 1/17/2008 130.29 39.11-1.02%-0.08% 1/18/2008 128.96 39.08-1.02%-2.56% 1/22/2008 127.65 38.08 2.40%-0.60% 1/23/2008 130.71 37.85 0.85% 3.25% 1/24/2008 131.82 39.08-1.45%-0.67% 1/25/2008 129.91 38.82 1.65% 2.16% 1/28/2008 132.06 39.66 0.50% 0.45% 1/29/2008 132.72 39.84-0.74%-0.35% 1/30/2008 131.74 39.7 1.82%-0.08% 1/31/2008 134.14 39.67 1.61% 1.61% 2/1/2008 136.3 40.31-1.26% 0.74% 2/4/2008 134.58 40.61-2.67%-3.62% 2/5/2008 130.98 39.14-0.81%-1.66% 2/6/2008 129.92 38.49 0.66% 1.01% 2/7/2008 130.78 38.88-0.64% 1.77% 2/8/2008 129.94 39.57 0.52% 2.96% 2/11/2008 130.61 40.74 0.93%-0.32% 2/12/2008 131.82 40.61 1.02% 2.49% 2/13/2008 133.16 41.62-0.88%-0.31% 2/14/2008 131.99 41.49-0.02%-0.51% 2/15/2008 131.96 41.28 0.28% 2.57% 2/19/2008 132.33 42.34 0.30% 1.49% 2/20/2008 132.73 42.97-0.84%-2.58% 2/21/2008 131.62 41.86 0.62% 1.05% 2/22/2008 132.43 42.3 1.26% 2.88% 2/25/2008 134.1 43.52 0.75% 1.47% 2/26/2008 135.11 44.16-0.10%-0.86% 2/27/2008 134.97 43.78-0.98% 1.60% 2/28/2008 133.65 44.48-2.23%-3.12% 2/29/2008 130.67 43.09-0.24% 0.93% 3/3/2008 130.36 43.49-0.38%-1.66% 3/4/2008 129.86 42.77 0.63% 2.62% 3/5/2008 130.68 43.89-2.07%-1.98% 3/6/2008 127.98 43.02-1.03%-1.77% 3/7/2008 126.66 42.26-1.32%-1.56% 3/10/2008 124.99 41.6 3.59% 3.92% 3/11/2008 129.48 43.23-0.93%-0.99% 3/12/2008 128.27 42.8 0.23%0....
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Module4_PortMgmt_Lecture - Course Outline I Index Models...

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