# Yield Beta Calculation- RM of Futures and Forwards

hi Guys,

Can anyone explain the calculation of Effective Beta please -

Alagan Santhianathan, equity strategist at Pradesh & Partners, believes the market will do well over the next six months and wants to increase the beta from 0.80 to 1.25, on the firm’s \$250 million portfolio. The beta on futures contracts is 1.05 with a price of \$250,000.

Another strategist, Jim Michaels, warns that hedging with futures contracts is not perfect because of the need to round to the nearest whole contract. The firm ends up buying the required number of contracts to achieve a 1.25 beta. Near the expiration of the contracts, the index has increased by 2% while the portfolio value has increased by 1.6% and the value of the futures has increased to \$255,250 per contract. B. Calculate the effective beta on the portfolio. Show your calculations.

Thanks,

3.2 = Risk management with Futures.

Apparently I forgot how to do this

Let me know if this is correct

(1.25-.8)/1.05 * (250,000,000/250,000) = # of futures to buy ~ 429

Gain on futures = 429 (255,250-250,000) = 2,252,250

1 Way:

Divided by portfolio value (250M) = .9009%

Port gain = 1.6%

Total gain = 1.6% + .9009% = 2.5009%

Index gain = 2%

Effective beta = 2.5009/2 = 1.25045 which is pretty close to 1.25.

Another way:

Portfolio gain = 250,000,000(1.016) + 2,252,250 (Future gain) = 267,252,250

Another way:

(250,000,000*(1.016) + 2,252,250) /250,000,000 = Overall Gain % = 2.5009.

2.5009/2 = 1.25045

the solution which I am following is this:

hedged port ending value =unhedged port ending value +Gain/Loss on contracts

=(250,000,000*1.016) + 429(255,250-250,000)=254,000,000+2,253,250=256,252,250

Hedged port return = hedged port EV /Hedged port BV=( 256,252,250/250,000,000)-1= 2.5%

Effective Beta= % change in port value/ % change in index = 2.5/2 =1.25

Thanks

So are you looking for intuition behind why it is the way it is? Not sure I can give an effective intuition behind that.

I could not understand the solution, so went back to books and relearnt and redid it.