Concepts Description
Risk Management : Applications of Forward and Futures Strategies
Adjust portfolio beta ‐ Stock
𝐶𝑜𝑣 𝑖, 𝑚
𝛽
𝜎
Numbers of contracts to adjust beta
𝛽 𝛽 𝑉
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠
𝛽 𝑃
Adjust portfolio duration ‐ Bonds Number of contract to adjust duration
𝑀𝐷 𝑀𝐷 𝑉
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑌𝑖𝑒𝑙𝑑 𝑏𝑒𝑡𝑎
𝑀𝐷 𝑃
Hedge portfolio ending value Hedged portfolio ending value = Unhedged ending value + G/L on contracts
Effective beta %∆𝑉
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑏𝑒𝑡𝑎
%∆𝑉
Basis risk Hedge is not perfect, due to basis risk :
‐ Number of contracts sold are rounded up to the nearest whole number
‐ Ex post valuation is not at contract expiration
‐ Performance of the portfolio / index could be different from ex ante beta
‐ Future / Spot price is not fairly priced based on cash and carry arbitrage model
‐ Numerator / Denominator are not based on same items
+ Stock : hedge using contract based on S&P500
+ Bond : hedge using T‐bond contract based on a single deliverable T‐bond
Preinvesting / Preinvesting : buy contracts in advance for cash that will be received in the future
Synthetic positions Synthetic positions : replicate an investment + end results using derivatives
‐ Synthetic equity / bond position = long contract + hold sufficient cash equivalent to earn risk‐free rate to pay for the contract at expiration
Exchange rate risk 1. Transaction exposure : when there is exchange of CF at a future date → can be hedged with deriva ves
‐ Receive foreign currency : sell forward contract on foreign currency
‐ Pay foreign currency : buy forward contract on foreign currency
2. Translation exposure : when convert FS to another currency
3. Economic exposure : when currency volatility affect competitive aspect of a business
Limitations on hedging FX rate risk Investment in foreign equity has :
‐ Market risk : change in investment position due to the business activity → hedge by selling forward contracts on foreign market index
‐ Currency risk : uncertainty from change of FX rate → hedge by selling forward contracts on foreign currency
Strategies for hedging currency risk :
‐ Hedge min future value, below which the portfolio is expected not to fall → s ll expose to value above that
‐ Hedge estimated future value of portfolio → if loss, it is overhedged
‐ Hedge the principal → not hedge the gain
Hedge with Futures / Forwards Differences between futures and forwards :
‐ Futures : standardised in amount and expiration date ; Forwards : Customised in amount and expiration date
‐ Futures : exchange with clearinghouse → no couterparty risk ; Forwards : have counterparty risk
‐ Futures : more regulated + transparent, require margin
, Concepts Description
Risk Management : Application of Option Strategy
Covered Call Covered Call : buy underlying asset + sell call option → Generate addi onal income from op on premium
Protective put Protective put : Buy underlying asset + buy put option → limit downside risk
Bull call spread Bull call spread : Purchase call option @ low exercise price + Sell a call option @ high exercise price
‐ Expect market price to rise
‐ limit downside risk
‐ limit upside potential if underlying rise
Bear call spread Bear call spread : Purchase call @ high exercise price + Sell call@ low exercise price
‐ Expect market price to fall
‐ Limit downside risk
‐ Limit upside potential if underlying decline
Bear put spread Bear put spread : Buy put @ higher exercise price + Sell put @ lower exercise price
‐ Expect market price to fall
Butterfly calls spread Butterfly calls spread :
‐ Buy 1 low exercise price call
‐ Buy 1 high exercise price call
‐ Sell 2 medium exercise price calls
Butterfly puts spread Butterfly put spread :
‐ Buy 1 low exercise price put
‐ Buy 1 high exercise price put
‐ Sell 2 medium exercise price puts
Profit pattern : same with butterfly calls spread
Risk Management : Applications of Forward and Futures Strategies
Adjust portfolio beta ‐ Stock
𝐶𝑜𝑣 𝑖, 𝑚
𝛽
𝜎
Numbers of contracts to adjust beta
𝛽 𝛽 𝑉
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠
𝛽 𝑃
Adjust portfolio duration ‐ Bonds Number of contract to adjust duration
𝑀𝐷 𝑀𝐷 𝑉
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑌𝑖𝑒𝑙𝑑 𝑏𝑒𝑡𝑎
𝑀𝐷 𝑃
Hedge portfolio ending value Hedged portfolio ending value = Unhedged ending value + G/L on contracts
Effective beta %∆𝑉
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑏𝑒𝑡𝑎
%∆𝑉
Basis risk Hedge is not perfect, due to basis risk :
‐ Number of contracts sold are rounded up to the nearest whole number
‐ Ex post valuation is not at contract expiration
‐ Performance of the portfolio / index could be different from ex ante beta
‐ Future / Spot price is not fairly priced based on cash and carry arbitrage model
‐ Numerator / Denominator are not based on same items
+ Stock : hedge using contract based on S&P500
+ Bond : hedge using T‐bond contract based on a single deliverable T‐bond
Preinvesting / Preinvesting : buy contracts in advance for cash that will be received in the future
Synthetic positions Synthetic positions : replicate an investment + end results using derivatives
‐ Synthetic equity / bond position = long contract + hold sufficient cash equivalent to earn risk‐free rate to pay for the contract at expiration
Exchange rate risk 1. Transaction exposure : when there is exchange of CF at a future date → can be hedged with deriva ves
‐ Receive foreign currency : sell forward contract on foreign currency
‐ Pay foreign currency : buy forward contract on foreign currency
2. Translation exposure : when convert FS to another currency
3. Economic exposure : when currency volatility affect competitive aspect of a business
Limitations on hedging FX rate risk Investment in foreign equity has :
‐ Market risk : change in investment position due to the business activity → hedge by selling forward contracts on foreign market index
‐ Currency risk : uncertainty from change of FX rate → hedge by selling forward contracts on foreign currency
Strategies for hedging currency risk :
‐ Hedge min future value, below which the portfolio is expected not to fall → s ll expose to value above that
‐ Hedge estimated future value of portfolio → if loss, it is overhedged
‐ Hedge the principal → not hedge the gain
Hedge with Futures / Forwards Differences between futures and forwards :
‐ Futures : standardised in amount and expiration date ; Forwards : Customised in amount and expiration date
‐ Futures : exchange with clearinghouse → no couterparty risk ; Forwards : have counterparty risk
‐ Futures : more regulated + transparent, require margin
, Concepts Description
Risk Management : Application of Option Strategy
Covered Call Covered Call : buy underlying asset + sell call option → Generate addi onal income from op on premium
Protective put Protective put : Buy underlying asset + buy put option → limit downside risk
Bull call spread Bull call spread : Purchase call option @ low exercise price + Sell a call option @ high exercise price
‐ Expect market price to rise
‐ limit downside risk
‐ limit upside potential if underlying rise
Bear call spread Bear call spread : Purchase call @ high exercise price + Sell call@ low exercise price
‐ Expect market price to fall
‐ Limit downside risk
‐ Limit upside potential if underlying decline
Bear put spread Bear put spread : Buy put @ higher exercise price + Sell put @ lower exercise price
‐ Expect market price to fall
Butterfly calls spread Butterfly calls spread :
‐ Buy 1 low exercise price call
‐ Buy 1 high exercise price call
‐ Sell 2 medium exercise price calls
Butterfly puts spread Butterfly put spread :
‐ Buy 1 low exercise price put
‐ Buy 1 high exercise price put
‐ Sell 2 medium exercise price puts
Profit pattern : same with butterfly calls spread
