synthetic cash from equity

CFA Level III Derivatives
#1

From Schweser, example on page 144 of book 4.

Manager B has a large position in UK stocks that are similar to a major UK stock index. She wishes to create GBP 15,000,000 of synthetic cash earning 2.0% for a six-month period. The futures index contract is priced at 3,700 with a multiplier of 10. The stock have a dividend yield of 3.0%.

The answer is sell 409 contracts and invest GBP 14,983,903 in Rf assets.

If we’re not selling our equity holdings, where the hell do we get the GBP 14,983,903 to invest in Rf assets? Also, the dividend yield of 3.0% is not considered in the schweser answer - is this simply extraneous information or an error on their part??

Thanks all.

#2

It’s a synthetic investment in cash, so no real cash needed. The wording however might be seen as a little ambiguous…

Dividend yield is not needed. You need it only to discount how many synthetic stocks you have bought or sold at the present time.

#3

When you buy a futures contract you don’t pay anything upfront, you just need to post initial margin. At contract expiry, you settle in cash or a physical delivery (depending on the asset).

So if you have 15m and want to create a synthetic long position, you will keep your 15m in cash and you can invest them to earn Rf over the 6 months period.

If you had actually invested the 15m to have the equity exposure, it would not be called a “synthetic” position

#4

In this case we have equity to synthetic cash so your answer is a little bit off

#5

Dividend yield is already included in the 409 contracts.

Without dividend, the number of contract is 405.4. Dividend 3% discounted at Rf 2% for 0.5 year gives the extra 4.5 contracts.

#6

I think it’s simpler than that.

How many contracts are needed to replicate 15m earning 2% over 6 months? First, work out the future value of 15m in 6 months = 15.15m

Then divide that by the price of a contract to get the # of contracts = 15.15m / 37k = 409. Done!

More complex bit:

Now, if you want prove that 409 contracts is synthetically equivalent to investing 15m in cash equivs for 6 months, you’d need to know what the market ending value is. Let’s pretend it’s 3500 (3700 is the beginning value).

409 * 37000 is 15.133m. Today that’s worth 14.984m using the 2% rf rate. Thus, if you’d invest that in cash for 6 months at 2%, you’d have 15.133m

So, we bought 409 contracts, and the multiplier was 10 (think of this number as # of shares per contract) = 4090 shares, this represents the # of terminal shares at the end of 6 months.

The market went down from 3700, to 3500. We sold contracts, so we made a gain of (3700 - 3500)(4090) = 818k

The ending shares are worth (4090)(3500) = 14.315m

Total = 14.315m + 818k = 15.133m

That’s equal to investing in cash!

The only time you’d need the dividend yield, is if you were asked what the equivalent number of shares required today you’d need to replicate the above. You worked out your terminal number of shares as 4090, so bring that back to today using the dividend yield of 3% over 6 months = 4030. If you bought 4030 shares today, you’ll earn 3% dividend yield, resulting in 4090 in 6 months.

#7

Simple answer: the futures price is spot price compounded at the risk-free rate to contract expiration. At contract expiration the futures price will converge to spot, nullifying any equity return and leaving you with just the risk-free rate. Some call it “implied borrowing rate”.