# SS15 Risk management

Portfolio with 35% bond and 65% stock and market value of 200 mil. Beta of stock 1.15 and modified duration of bond 6.75. Manager wishes to increase stock allocation to 85% and reduce bond to 15%. In addition to altering asset allocation, the manager would like to increase the beta on stock position to 1.2 and increase the bond modified duration to 8.25. Stock index future contract priced at 157,500 and has beta at 0.95. Bond future contract is priced at 109,000 and implied modified duration of 5.25. The stock future contract has a multiplier of one.

A. Calculate the number of contracts manager should go long or short. (stock and bond) to achieve his goal.

-393 bond contracts

364 stock contracts

Sell 40 million bond

40m x (0-6.75)/(5.25x109000)= --471.82

tune remaining bond duration:

30m x (8.25-6.75)/(5.25x109000) = 78.637

Net: -393

40m x (1.2)/(0.95x157500) = 320.8

Tune existing stock beta

130m x (1.2-1.15)/(0.95x157500) = 43.44

net: 364

You are correct…

However, i have another question.

When we adjust to achieve the new beta and duration requirement (by buying additional 43 stock f contracts and reduce short f bond by 79, is the new allocation of stock/bond 85/15?

it is tricky if you want to talk about allocation.

The allocation of your portfolio never changed. This is also the point of this tuning of betas and durations using futures.

you portfolio allocation always stays the same. It is only the “synthetic” allocation that we must keep track of when we deal with this type of questions.

if you can follow the logic behind each calculation, then you are good.

just remember this - change the difference between current to desired to cash (remove beta and duration to nil) - then add exposure with futures to make it reflective of desired.

Thanks passme. I understand that the (actual) allocation never change (kept 65/35). However, there are 2 requirement here, the 1st - changing to (synthetic) portfolio with allocation of 85/15 and the 2nd is change beta and duration.

we do the 1st step (by selling 40mil value of bond F contracts and long stock f contracts) - the synthetic P now be 85/15

The 2nd step to adjust the new (synthetic) bond (allocation) and stock to target duration and beta. So is that the 2nd step action impacts the new allocation of synthetic portfolio?

I think if we do the 2 step together, the synthetic allocation not be 85/15.

I have the same question as Truongdv. Especially after we look at the second question, why does 130/70 + future contracts have the same market value of portfolio as 170/30 allocation?