Difference in expected loss from protective put strategies

Hi everyone,

Can somebody please confirm the answer for this question?

There is a 20% chance the stock price goes up to $42.00, a 20% chance it goes up to $44.00, and a 60% chance it falls to $36.00.

What is the difference in expected loss from protective put strategies using Dec 38 and Dec 39 puts?

Exhibit 1

Current Stock Price: $41.28 Size Holding: 140,000 shares Dec 39 Put Price: $4.20 Dec 38 Put Price: $3.62

This was in Schweser’s Exam 2 morning right? I remember this question.

Yes. can you please confirm if the solution is correct?

For a single share:

$39 strike:

  • Cost = $4.20
  • Expected payoff = 0.6 × ($39 − $36) = $1.80
  • Expected profit: $1.80 − $4.20 = −$2.40

$38 strike:

  • Cost = $3.62
  • Expected payoff = 0.6 × ($38 − $36) = $1.20
  • Expected profit: $1.20 − $3.62 = −$2.42

Each sounds pretty bad.

This is the answer from the curriculum. My concern is why the expected loss for the Dec 38 put is 966,000. Isn’t it has to be $854,000? and the net is $53,200?

Expected stock price:(0.2 × 42) + (0.2 × 44) + (0.6 × 36)= $38.80

Expected loss using Dec 39:[(41.28 - 39) + 4.20] × 140,000= $907,200

Expected loss using Dec 38:[(41.28 - 38) + 3.62] × 140,000= $966,000

Dec 39 loss smaller by:966,000 - 907,200= $58,800

Hi S2000magician or anyone,

In this scenario we’re longing a put however the answer in the back for the expected loss includes a “+” for the put premiums. If we’re BUYING puts, wouldn’t we subtract the put premium since it’s a cost?

Answer in back of book.

Expected stock price:(0.2 × 42) + (0.2 × 44) + (0.6 × 36)= $38.80

Expected loss using Dec 39:[(41.28 - 39) + 4.20] × 140,000= $907,200

Expected loss using Dec 38:[(41.28 - 38) + 3.62] × 140,000= $966,000

Dec 39 loss smaller by:966,000 - 907,200= $58,800

they are just reversing the sign, if you put a minus sign in you would get the same answer. However, is $58,800 correct answer? For the Dec 38, the expected loss is $854,000 from my calculation. Thus, the net should be $53,200. Can someone please confirm?

Sorry; I was simply thinking about the profit/loss on the put, not on the underlying stock.

I don’t understand what they’re doing (i.e., what you wrote as “answer in back of book”).

With the $39 puts there’s a:

  • 20% chance that your portfolio will be worth $44/share
  • 20% chance that your portfolio will be worth $42/share
  • 60% chance that your portfolio will be worth $39/share

So the expected value of your portfolio is 0.2($44) + 0.2($42) + 0.6($39) = $40.60. So the expected profit (loss) per share is $41.28 − $40.60 − $4.20 = ($4.88)/share, or ($4.88) × 140,000 = ($683,200) total.

With the $38 puts there’s a:

  • 20% chance that your portfolio will be worth $44/share
  • 20% chance that your portfolio will be worth $42/share
  • 60% chance that your portfolio will be worth $38/share

So the expected value of your portfolio is 0.2($44) + 0.2($42) + 0.6($38) = $40.00. So the expected profit (loss) per share is $41.28 − $40.00 − $3.62 = ($4.88)/share, or ($4.90) × 140,000 = ($686,000) total.

The difference is $2,800, with the $39 puts winning.

Hi Magic,

Can you please explain the reasoning behind using $39 for Dec 39 put, and $38 for Dec 38 put? I don’t get this.

I thought that that’s what you meant by the 38 and 39.

Did you mean something else?

I think 38 and 39 here should be the strike price of the put option. Don’t we have to find the expected stock price, then use it to find the payoff from the protective put strategy? Below is the complete passage from the mock paper.

One reason for the hiring is that AHI’s CIO is interested in the use of protective puts to mitigate risk in equity portfolios. Specifically, Ramiro has been asked to demonstrate how a protective put could be used to hedge the risk of AHI’s holding in Allavate, Inc. (ALL), a pharmaceutical company that has had a very strong run on the back of several successful anti-allergy drugs.

However, AHI is concerned that ALL’s product pipeline has a relatively small number of new drugs, and any downward correction in the general market could have a significant negative impact on ALL’s stock price. AHI’s analysts have estimated that there is a 20% chance the stock price goes up to $42.00 by expiry of the CBOE-traded December options on the stock, a 20% chance it goes up to $44.00, and a 60% chance it falls to $36.00.

Ramiro has been asked to calculate the expected loss of a protective put strategy using the expected stock price and either Dec 38 or Dec 39 puts as shown in Exhibit 1.

Exhibit 1: ALL Stock and CBOE Option Prices

Current Stock Price: $41.28 Size Holding: 140,000 shares Dec 39 Put Price: $4.20 Dec 38 Put Price: $3.62

How are you getting 854k as the expected loss for the Dec 38 put?

38 is the strike, so 41.28 - 38 = 3.28 is the loss from the long stock position, and 3.62 is the cost of the put option. If you add those two to get 6.9 and multiply by the 140k, you get 966k. Do the same for the Dec 39 protective put.

its cool. i know where i did wrong now

Ah ok glad to hear

I also get $854,000 loss for the Dec 38 Put Thanhnguyen504. I don’t understand why they calculate 41.28-38. If the stock drops bellow the final stock price of 38.8 then you won’t exercice your put and sell your position for the market price no?

can someone help?

Thanks!

The current stock price is $41.28.

The exercise price of the Dec 38 put is $38.

So $41.28 - $38 is the loss from the long position in the protective put. Anything below that and the loss in the long position is offset by exercising the put option. So, add the loss of $3.28 to the $3.62 cost of the option to get the $6.90 loss per share. Multiply that by 140k shares to get the (max) expected loss of 966k.

Still don’t understand how 854k is computed or the $38.8 figure you mentioned.

I calculated the final market price of the stock by using the % just over the exhibit 1: AHI’s analysts have estimated that there is a 20% chance the stock price goes up to 42$ by expiry a 20% chance it goes up to 44$ and a 60% chance it falls to 36$ which when you add those up it gives you 38.8$ at expiry.

I also had a problem with this question.

It seems to me, they calculate the max. expected loss on both the $38 and $39 PPs without taking into account the expected price of $38.8

If we leave out of consideration the expected price, then our maximum expected loss is:

X - S0 - p

for the $38 put: 38 - 41.28 - 3.62 = - 6.9 x 140,000 = - 966,000

for the $39 put: 39 - 41.28 - 4.2 = - 6.48 x 140,000 = - 907,200

These are the official answers.

BUT if you calculate with the expected price of 38.8, the $39 put will be called, but the $38 put NOT, and your payoff will be:

38.8 - 41.28 - 3.62 + zero = - 6.1 x 140,000 = - 854,000

Now I would be glad to hear what am I doing wrong???

Yes i believe the question does not mention it specifically, but it’s asking for MAX expected loss.

It then compounds the possibility of confusion by mentioning the expected stock price will be used (in the vignette) and providing the calculation for the expected price of $38.8 in the answer.

I’d ignore the wording and focus on knowing the max expected loss, per the LOS.

Sorry guys - need to bump this. I don’t agree with your conclusion. The vignette clearly says “has been asked to calculate the expected loss of a protective lit strategy USING THE EXPECTED STOCK PRICE”

THEREFORE: In the case of the December 38 put - it would not be exercised and your loss would only be 41.28 - 38.8 (which is the EXPECTED STOCK PRICE)

They are wrong on this.