2024.02 CFA III MOCK B First Session
No.PZ2023122601000007
Calculate the value of the variance swap six months from initiation.
he value of a variance swap at time t is given by the formula:
Volatility strike on existing swap = 21
Variance strike on existing swap = (Volatility) 2 = 212 = 441
Variance Notional = Vega Notional / (2 × Strike) = $22,000,000/ (2 × 21) = $523,810
Realized Volatility = 272 = 729
Implied Volatility = 232 = 529
t = 6 months
T = 12 months
Present value interest factor (PVIF) after six months (discounting for six months where the annual interest rate is 4.75%)
PVt(T) = 1 / [1 + (4.75% × (6/12))] = 0.977
Var Swap = $523,810 × 0.977 × {(6/12) × 729 + (6/12) × 529 – 441}= $523,810 × 0.977 × 188 = $96,211,238.10 = $96,211,238
Given that AJ Capital is long the variance swap, the mark-to-market value is positive for AJ Capital.
如何确定的Implied Volatility？为什么不能是21呢？而是23呢？
下面是题目
Sean Galligan is a currency management consultant. Galligan’s consultancy efforts include investment portfolio analysis, the calculation of hedge ratios for currency exposure, and the generation of currency alpha through active foreign exchange management. Galligan’s clients include investment banks, registered investment advisors, hedge funds, asset managers, and institutional investors.
AJ Capital, an investment bank based out of Miami, Florida, hired Galligan to help find profitable opportunities in the market. Ajay Suri, CEO of AJ Capital, is concerned about the Federal Reserve’s monetary policy stance for the upcoming six months and anticipates increased volatility in the equity markets. Suri requests that Galligan devise a strategy to generate alpha by taking a directional bullish view on the volatility, but with minimal cost to the firm. Galligan gathers information presented in Exhibit 1 and recommends buying a one-year variance swap on the Russell 2000 Index
Six months after taking the long position in the variance swap, the Russell 2000 Index has recorded a realized volatility of 27%. On the same day, Galligan identifies a new six-month variance swap on the Russell 2000 Index with a fair strike of 23%.
Six months after taking the long position in the variance swap, Suri’s bullish directional view on the volatility has changed. Suri believes that the volatility has peaked and expects the volatility to remain range bound for the upcoming six months. Suri requests that Galligan now recommend how to mitigate volatility exposure. Galligan makes the following recommendations based upon an expectation of a range bound volatility market.
Recommendation 1: Implement a long volatility straddle that is delta neutral and likely to be profitable.
Recommendation 2: Implement a net short volatility options strategy, which will earn option premiums from out-of-the money expiring options.
Chain Investments, another client of Galligan’s, is a crypto currency asset management firm located in Paris, France. Chain Investments has an equity cryptocurrency investment fund (ECIF) that invests in cryptocurrency-related equity investments across the globe. ECIF uses EUR as its reporting currency and holds assets in various currencies, such as EUR, GBP, and USD. Gabriel Durand, CIO at Chain Investments, is concerned about recent scrutiny of crypto businesses by US regulators and intends to hedge ECIF’s USD exposure. Durand requests Galligan to suggest a suitable hedging option. After reviewing ECIF’s USD exposure and currency volatility characteristics in Exhibit 2, Galligan recommends implementing a minimum-variance hedge.
