1. © K.Cuthbertson and D.Nitzsche 1 Lecture Stock Index Futures Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK MANAGEMENT (J. Wiley, 2001) K. Cuthbertson and D. Nitzsche

2. © K.Cuthbertson and D.Nitzsche 2 Topics Basic Concepts Speculation Hedging

3. © K.Cuthbertson and D.Nitzsche 3 Basic Concepts

4. © K.Cuthbertson and D.Nitzsche 4 Stock Index Futures:Terminology Hold, TVS 0 = $2m in diversified equity portfolio and ‘stock index’ S 0 = 200 Number of index units in stocks,N s =TVS 0 /S 0 =10,000 “shares” ie. For each unit change in the index S, then the value of the stock portfolio changes by $10,000 (DOLLARS)  (TVS) t = N s  S t

5. © K.Cuthbertson and D.Nitzsche 5 F 0 = 202 z = contract size = $500 per index point - for S&P 500 Then the face value of one futures contract is FVF 0 = z F 0 = $500 ( 202 ) = $101,000 Fear a fall in equity prices : what do I do to hedge ? Short the futures How many futures contract do I short ? Stock Index Futures:Terminology

6. © K.Cuthbertson and D.Nitzsche 6 Specualtion

7. © K.Cuthbertson and D.Nitzsche 7 Figure 3.2 : Speculation: Nikkei index (Leeson) Leeson buys Leeson closes out / sells ‘Five eights make $1.4bn ?’

8. © K.Cuthbertson and D.Nitzsche 8 Hedging with Stock Index Futures

9. © K.Cuthbertson and D.Nitzsche 9 Minimum Variance Hedge Ratios  V = change in spot market position + change in futures position = N s.(S 1 -S 0 ) + N f (F 1 - F 0 ) z = N s.  S + N f (  F) z where, z= contract multiple ($500 for S&P 500)  S = S 1 - S 0,  F = F 1 - F 0 The variance of the hedged portfolio is

10. © K.Cuthbertson and D.Nitzsche 10 Minimum Variance Hedge Ratio(1)   is the regression “beta” for the absolute change in your portfolio ‘price’ S regressed on the absolute change in F: ie.   =  (  S,  F)/  2 (  F) =   (  S)/  (  F) Choose N f to minimize variance, gives:

11. © K.Cuthbertson and D.Nitzsche 11 Minimum Variance Hedge Ratio-(2)  p is the regression “beta” for the percentage change in your portfolio S (ie. the portfolio ‘return’) regressed on the percentage change in F. In practice hedging error arises because  p is an estimate and may not hold over the future. Equivalent expression

12. © K.Cuthbertson and D.Nitzsche 12 End of Slides