Synthetic Cash from Equity Futures

I obtained this question from a previous mock exam (2009 CFA Level 3 PM Question 47)

  1. To achieve Jeffrie’s objective, the number of US mid-cap equity futures contracts that Michael will sell is closest to?

A. 319

B. 322

C. 332

The portfolio is 75,000,000. The US Risk Free rate is 4% annually and the time period is 3 months or 0.25 years. The beta of the portfolio is 1.2.

The associated mid cap future has a contract price of $2,350, multiplier of $100, and beta of 1.29.

The solution completely ignores the Beta. My question is why do we ignore the beta information for both the future and portfolio.

Solution: Number of Futures = -75,000,000 * 1.04^(0.25)/235,000 = - 322

Ans should ve been arnd 300 keeping betas

generating synthetic cash is different from reducing the equity position.

reducing the equity position - would involve the betas.

synthetic cash - what they have done is the right approach.

ya u r right!

investor has equity position & looking to convert it into synthetic cash for 3 months> by shorting furtures, mentioning about beta in the question they take you away from answer.

Ans shud be short 322.22 (unrounded) or 322 (rounded) no of futures. Effectively 322*2350*100=75,670,000 or 74,931,66 (75,670,000 /((1.04)^0.25) in todays term

Can you elaborate a little on why? What is synthetic cash and how is it different from cash that you do not incorporate beta?

The discussion in the CFAI text left that very vague.

Jut to add some color to this thread , the CFAI exam referred to also stated that the index had a beta of 1.2 while the futures contract had a beta of 1.29 . However even if you use those numbers the answer is still same ( within big rounding error )

the only part where the color goes off is that it would be missing the 1.04^0.25 in the case of using the betas… and if the answers are quite close - we would get thrown off to the wrong answer.

Remember this is not a hedging operation , because you intend to hold the futures contract to expiry . Your goal is just to raise cash ( earn risk free rate ) and nothing else. At the futures expiry the contract will converge to the index price , so the risk of your short position is virtually zero .

It would be different if you are trying to hedge some or all of the equity position and then you would have to consider the betas and probably have to even consider it frequently

Wait a sec. According to our friend Don Chance (vol 5, page 363) the beta of the stock portfolio and the futures contract must be the same to ignore the beta. Otherwise,

75 m x 1.04^.25 -1.20 ----------------------- x ----------- = 299.81 or 300. 2350 x 100 1.29

I’m guessing in 2009 the approach might have been different

If you incorporate beta and only sell 300 futures contracts then you would still have a large equity exposure. These questions should be easier because there is a simple check you can do:

assuming that the index does not change, index = 2350 in 3 months, your monitized position should approx equal 75,000,000 * 1.04^0.25 or 75,739,005.

if you only sell 300 contracts your future position is: 300*2350*100 = 70,500,000

if you sell the correct 322 contracts your future position is 322*2350*100 = 75,670,000

obviously this doesn’t account for any reinvestment of dividends which would need to be included for an accurate calc, but you can see that the 322 contracts monitizes the equity better than the 300.

Wait a minute.

Your goal is not to eliminate the exposure ( risk ). If that was the case you would look at Betas closely , even daily , to keep the risks in line and close to zero.

Your goal is simply to monetize your equity position .This means your intention is to conevrt your current position to cash ( to earn a risk free rate ) and then redeem the cash upon expiry .

If you had other dreams ,you could not sleep at night , given the risks. This operation is essentially risk free because your short is fully covered at expiry ( due to futures converging to spot at expiry )

Fin and jana, I think you both may be incorrect.

300 futures should be correct because it controls approximately the same amount risk, and you have to match the risk to create synthetic cash.

Here’s my proof.

For futures: 300 x 235,000 x 1.29 = $90,945,000

For stock 75 million x 1.2 x 1.045 ^.25 = $91 million

Hank , your calculations of the cash resulting from selling futures is incorrect.

If you sell 300 futures contracts each priced at $235k you will get $70.5 million .

It does not matter what the beta is . The price is not contingent on beta.

Similarly if you monetized the stock you would generate $75 k only and it would be independent of beta.

Okay, my grip on this is less than 100%. But how do you deal with the residual beta?

IMHO , the beta would indicate the riskiness of the asset. ( in terms of how volatile its price could be ). If you own $75k of stock and short approx $75 k of futures , from that point on , your long stock position and your cash investments ( earning risk free rate ) would track the short futures position at the horizon ( which is expiry of the futures ).

You know that the 322 or so Futures contract would converge in price to the value of your stock position . In fact if your horizon is exactly the futures expiry , you could take that to the bank literally. So at expiry you are completely covered . To cover the short , you simply hand over to the long your entire equity position which would be at the same price ( convergence ).

Meantime you’ll have cash left ( original cash plus interest ). Of course , this cash could be less than the value of the equity position you’re handing over to the holder of the long , because that has grown a lot. Or it could be worth more than the equity position , because the equity position has dropped in value. Either way you will earn only a risk free rate and have a position that is equal to monetized position 3mths ago plus risk free.

You will earn no more and no less than the risk free rate within the horizon

Yes, the whole intention was only to earn atleast risk free rate in view of a bleak outlook of economy without exposing to any risk. Since PM has no view lets say for the next three months, she’s better off atleast earning risk free on portfolio.

Stock – Cash = Futures or Stock - Futures = cash

You own the stock you sell future, you earn cash return

Also in book, whenever equitizing to cash from equity or to equity from cash, beta values are not used.

Here stock portfolio & index betas r identical

P No 363 para below blue box" you might be wondering…both cases" does talk about why the beta values are not used. ??

So, given p363, how can we ignore the OP’s different betas?

This is precisely the point of using short futures. if your firm opinion is that equities will earn less than the risk free rate for the next 3 months , but you do not want to lose time and energy and costs in selling off your equity positions ( or want to retain the positions you have built up with great difficulty and cost ) , you can go to (synthetic) cash for the next 3 months using futures.

Your alternative is spend a lot of time , costs and risks selling off your positions one by one and then do the reverse after 3 months are up ( buy them all back ).

Or be selective by selling some of them and holding some of them until your beta is roughly matched to the index.

If you did this, then you have to worry about betas and delta hedging and spend many a sleep less night wondering if you have balanced the risks fully.

The futures give you a one-shot , no questions , no more and no less option of earning the risk free rate