Risk Management Using Forwards and Futures

Implied duration uses implied yield as reference rate.

Implied Yield is the yield of the underlying bond as if it were delivered at the expiration of the futures contract (instead of the expiration of the bond)

So Delta Futures Price = Delta Implied Yield * (- implied duration) * Futures Price

Yield Beta = change of bond yield / change of implied yield

(B_t – B_p) * Portfolio Value = B_f * Futures value * # of contract

B_f = (B_t-B_p)/B_f * Portfolio Value / Futures value

Remember, Beta = cov(i, m)/ var(m), but also means ratio of index return to market return.

Synthetic Risk Free Asset = long stock – stock index futures (i.e. short futures)

Therefore,

Synthetic Equity = long risk-free asset + stock index futures (i.e. long futures)