Volatility derivatives in portfolio optimization

Transcription

1 Volatility derivatives in portfolio optimization Juliusz Jabªecki, WNE UW & NBP Joint work with: Ryszard Kokoszczy«ski, Paweª Sakowski, Robert lepaczuk & Piotr Wójcik FindEcon 2014

2 Exposure to volatility is natural in a delta hedged option... P/L = d (C(S) S) Θ t Γ S ΓS 2 t ( σ 2 Σ 2)

3 ... but such exposure isn't pure as the realized-implied spread is weighted by changing gamma A 1-year ATM call struck at implied volatility 30% and delta hedged daily (with µ = 0.12, r = 0.05 and S0 = 100).

4 Volatility derivatives give exposure to pure volatility......and have become an important asset class

5 Standard rationale for adding exposure to volatility Futures on implied volatility (VIX) exhibit strong negative correlation with equities Szado (2009):...the addition of 10% VIX futures cuts the losses to about 1/5 their initial level while reducing standard deviation by 1/3. Similar results found e.g. by Daigler & Rossi (2006); Dash & Moran (2007).

6 Long volatility exposure is costly in the long term Monthly roll cost = (1st - 2nd contract)/2nd contract; slope dened as 5th/2nd VIX futures - 1.

7 Volatility risk premium can oset roll cost Av. implied-realized spread 3 p.p.

8 Variance swap payo captures volatility risk premium VS Payo = Notional (RV 2 Variance strike 2 ) But no free lunch...

9 Does adding exposure to volatility improve portfolio risk/return prole? US stock market daily data covering period ; Start with a benchmark portfolio: US stocks S&P 500 total return index; US bonds long-term US Treasury bonds total return index (provided by Bloomberg); Add volatility exposure: implied volatility S&P Dynamic VIX Futures (provided by S&P); realized volatility rolled P/L on a theoretical 1M S&P 500 variance swap contract

10 Does adding exposure to volatility improve portfolio risk/return prole? US stock market daily data covering period ; Start with a benchmark portfolio: US stocks S&P 500 total return index; US bonds long-term US Treasury bonds total return index (provided by Bloomberg); Add volatility exposure: implied volatility S&P Dynamic VIX Futures (provided by S&P); realized volatility rolled P/L on a theoretical 1M S&P 500 variance swap contract

11 Does adding exposure to volatility improve portfolio risk/return prole? US stock market daily data covering period ; Start with a benchmark portfolio: US stocks S&P 500 total return index; US bonds long-term US Treasury bonds total return index (provided by Bloomberg); Add volatility exposure: implied volatility S&P Dynamic VIX Futures (provided by S&P); realized volatility rolled P/L on a theoretical 1M S&P 500 variance swap contract

12 Portfolio optimization: benchmark case Stocks & bonds Mean of Portfolio Returns Benchmark portfolio Stocks Bonds Standard Deviation of Portfolio Returns Optimal portfolio: stocks 40%, bonds 60%

13 Portfolio optimization: long VIX futures 0.16 Stocks, bonds & VIX futures 0.15 Mean of Portfolio Returns Optimal portfolio with VIX futures 0.07 Benchmark portfolio Standard Deviation of Portfolio Returns Optimal portfolio: stocks 46%, bonds 36%, VIX futures 24%

14 Portfolio optimization: VIX futures and variance swap 0.22 Stocks, bonds, VIX futures & variance swap Mean of Portfolio Returns 0.16 Optimal portfolio with VIX futures and variance swap Optimal portfolio with VIX futures 0.08 Benchmark portfolio Standard Deviation of Portfolio Returns Optimal portfolio: stocks 15%, bonds 14%, VIX futures 39%; variance swap 32%

15 Benchmark Benchmark+IV Benchmark+IV+VS Return Std. dev Sharpe ratio % VaR

16 Conclusions Volatility derivatives oer pure exposure to volatility (both implied and realized) We conrm the previous results that at least for the U.S. data exposure to implied volatility improves the benchmark portfolio eciency We also go beyond most studies by showing that the most benecial strategy combines exposure to both implied volatility and realized volatility. IV diversies market risk of the stocks portfolio allowing for positive returns even in the periods of stock market stress; exposure to RV through variance swaps allows pocketing the VRP and osets the roll cost of VIX futures.