Module4_PortMgmt_Lecture

# Module4_PortMgmt_Lecture - Course Outline I Index Models...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

Module4_PortMgmt_Lecture - Course Outline I Index Models...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online