Revision questions

[1495_sc]

While solving past year papers, I had few questions. Cab someone please help in clearing my doubts?

1. For option payoff, we were asked to draw a graph in past year papers. Given online exam, is this still a possibility?

2. Sept 2018- Q7, sector selection profit for Fund A should be -0.25%.

calculated as (total outperformance-stock selection profit) = (0.72%-0.98%) = -0.25%. Even when I calculated sector selection profit as (actual sector allocation- benchmark sector allocation)*(notional sector return- overall benchmark return) for each sector and sum it, the answer is -0.25%. Is this a mistake in examiner's report? Please help.

3. Q3-for butterfly spread and bear spread- I have few doubts.

Bear spread-

a) I did not understand the diagram completely.

Referring to the solution in examiner's report now.

A. For call option-We are considering 3 cases here, St>K2, St<K1 and K1<St<K2.

I presume that the second part of the graph (downward sloping part) is for case K1<St<K2 and the flat curve after that is for St>K2. If this is correct, shouldn't the curve be on the negative axis for St>K2?

Also, why is St>K2 assumed as a loss? Wouldn't this depend on the value of O1-O2 as payoff = (O1-O2)-(K2-K1)

B. For put option- again, we are considering 3 cases.

a) When St<K1, the payoff should be (O1-O2)+(K2-K1) and not (K2-K1) only, right?

Butterfly spread (part ii)

I couldn't follow the solution in examiner's report. Is there a more straightforward solution or relatable bookwork which I can apply to understand?

Thank you in advance!

 

[1495_sc]

Questions related to April 2018 diet.

1. In Q6. i) What if we calculate ratios as the question asks for assessment of balance sheet and income statement? Is it not required unless we are specifically asked to 'calculate'?

iii) Why is the solution focused around why the rival will purchase US Stores and not why it is willing to pay double the net assets amount for purchasing US Stores? Except for points like the property being undervalued, cost will be greater than 20,000 if they start from scratch, all points are just explaining why rival will purchase US Stores. Not related to the price being twice the net assets?

iv) The answer is generic. Should it not conclude with Sharpe and pre-specified SD measure if the portfolio represents whole universe of manager's wealth?

2. Why is convenience yield deducted to arrive at futures price for assets which are less widely held as investment? By definition; convenience yield is a positive value to the ownership of physical commodity.

Please help. Thank you!

 

[Joe Hook]

Dealing with the first post:

1) No we do not believe that drawing diagrams are a possibility in the exam.
2) Yes we believe there is a mistake in the examiners report so agree your stock selection of -0.25%.

For the bear spread, you are correct. The axes here aren't clear so there's nothing to suggest the lower part of the curve is not in negative territory. As for why there must be a loss for St>K2, this is the principle of no arbitrage. If it were possible to come up with a strategy where profit was guaranteed in all scenarios then this would represent risk-free profit and we assume that not to be possible for derivatives such as options.

Using put options, agreed there is a mistake in the examiners report here and it should be Y2 - Y1 + (O2 - O1)

For the butterfly spread you might be better with a numerical example. We'll ignore premiums for ease. Imagine call options with strikes 50, 60 and 70.

If we buy 1 call strike 50, sell 2 with strike 60 and buy 1 with strike 70.

Payoffs are:

0 if St < 50
St - 50 if 50 < St < 60
(St - 50) - 2(St-60) = 70 - St if 60 < St < 70
(St - 50) - 2(St-60) + (St-70) = 0 if 70 < St

This gives the level shape either side and the upward or downward sloping middle section.

Another way to put this would be the area to the left of the apex has the shape of a long call option. Then to the right of the apex we need to add something into the portfolio that not only flattens the line but starts to bring it back down so we need to take up a short position in TWO call options. Then at the point where it flattens again we need to neutralise the position so bring the portfolio up to two long call options by purchasing an option.

Not easy to get across via email this one. If you are still struggling I would strongly recommend having a go at building portfolios of options in excel. You can see up a column of share prices at maturity and then set up other columns for the payoffs of those different options at maturity and combine them together to create the types of diagrams we see here.

 

[Joe Hook]

For April:

Part (i), you could calculate ratios and you'd hope it would lead to the same conclusions as the answer. However, as you say we haven't specifically been asked to perform any calculations, and there's lots of information presented, so I would assume there was enough there to comment on without further calculation to earn the 8 marks.

In most SP5 questions there will be an element of generality and then some specifics. If the company taking over believes it can operate it better, or achieve higher values or make greater profits, then it will be willing to pay more for the company than the NAV would suggest. Now the fact they are willing to pay double doesn't really come into it. We'd need more information to know why exactly double is the right number, but we can make lots of comments about why they might pay more. So the examiners make a generic point of undervalue and then go on to a list a number of reasons the value of the company might be higher in the hands of the company taking over ie reasons they might be willing to pay over the NAV.

You are right that a convenience yield is a positive value to owning an asset. This convenience yield is built into the spot price of the asset, ie the price you would pay in the market to obtain the asset today. Futures are agreements to purchase assets in the future and so you are not benefiting from the convenience yield in the short term. Hence we strip out the convenience yield out of the spot price to get the futures price.

As an example, imagine that there is a short-term supply issue with oil e.g. ships stuck in the Suez canal. The price to buy oil today might shoot up to say $100 a barrel because it is in short supply, ie there is a convenience yield, but might be expected to return to normal levels in 6 months time so the futures price (the price at which we're agreeing to buy oil in 6 months time) is down at $60 a barrel say. So futures price = Spot price (100) + cost of carry (let's say 2) - convenience yield (42).

Joe

Joe

 

[1495_sc]

For the butterfly spread you might be better with a numerical example. We'll ignore premiums for ease. Imagine call options with strikes 50, 60 and 70.

If we buy 1 call strike 50, sell 2 with strike 60 and buy 1 with strike 70.

Payoffs are:

0 if St < 50
St - 50 if 50 < St < 60
(St - 50) - 2(St-60) = 70 - St if 60 < St < 70
(St - 50) - 2(St-60) + (St-70) = 0 if 70 < St

This gives the level shape either side and the upward or downward sloping middle section.

Another way to put this would be the area to the left of the apex has the shape of a long call option. Then to the right of the apex we need to add something into the portfolio that not only flattens the line but starts to bring it back down so we need to take up a short position in TWO call options. Then at the point where it flattens again we need to neutralise the position so bring the portfolio up to two long call options by purchasing an option.

Not easy to get across via email this one. If you are still struggling I would strongly recommend having a go at building portfolios of options in excel. You can see up a column of share prices at maturity and then set up other columns for the payoffs of those different options at maturity and combine them together to create the types of diagrams we see here.

This example was very helpful! I plotted a graph which matched the graph in the question.

However, while we are assuming the tail of first diagram in part i) to be on the negative axis, we are also assuming the tails of diagram in part ii) to be =0, not negative. Won't this be an inconsistent assumption between i) and ii)?

Most importantly, I would like to know the approach we should allow in an exam condition for constructing suitable call/put option portfolio matching a certain payoff. Is there any rule of thumb we should keep in mind? For example, how will we know that 'If we buy 1 call strike 50, sell 2 with strike 60 and buy 1 with strike 70', we will achieve the butterfly spread in the question?

This is not covered in Core Reading material. Please advise.

 

[1495_sc]

As for why there must be a loss for St>K2, this is the principle of no arbitrage. If it were possible to come up with a strategy where profit was guaranteed in all scenarios then this would represent risk-free profit and we assume that not to be possible for derivatives such as options.

Ok. We are also assuming that K1<St<K2 condition could be a profit or loss. If so, wouldn't this assumption suffice for no arbitrage principle? Why are we specifically assuming a loss for St>K2?

 

[1495_sc]

iv) The answer is generic. Should it not conclude with Sharpe and pre-specified SD measure if the portfolio represents whole universe of manager's wealth?

What about this one in April 2018, Q7 part iv)? Sorry, marked this as Q6 iv) originally.

 

[1495_sc]

Futures are agreements to purchase assets in the future and so you are not benefiting from the convenience yield in the short term.

Can you please elaborate? Does it mean that convenience yield is positive value currently but as futures are long term in nature, this convenience yield is not relevant? Hence, it is deducted.

Why is it relevant for only commodities not widely held as investment? Keen to know more about the practical aspect of this to make recalling this part easier.

 

[1495_sc]

Thanks a lot for clarifying my doubts!!

 

[Joe Hook]

This example was very helpful! I plotted a graph which matched the graph in the question.

However, while we are assuming the tail of first diagram in part i) to be on the negative axis, we are also assuming the tails of diagram in part ii) to be =0, not negative. Won't this be an inconsistent assumption between i) and ii)?

Most importantly, I would like to know the approach we should allow in an exam condition for constructing suitable call/put option portfolio matching a certain payoff. Is there any rule of thumb we should keep in mind? For example, how will we know that 'If we buy 1 call strike 50, sell 2 with strike 60 and buy 1 with strike 70', we will achieve the butterfly spread in the question?

This is not covered in Core Reading material. Please advise.

Inconsistent yes, but bear in mind that I constructed that situation without any allowance for premiums for simplicity. Once we factor in premiums then we should end up with some negative profits.

The Core Reading expects you to be able to construct option diagrams and diagrams for portfolios of options. This question tests your ability to take an portfolio diagram and identify it's constituent parts. So whilst you won't be asked to draw any diagrams (because the exam is in Word) a question such as this is a test of your ability to do so. So no rules of thumb here, just make sure you can draw payoffs and combine them together and this will help you identify any such profit shapes that come up in the exam.

 

[Joe Hook]

Ok. We are also assuming that K1<St<K2 condition could be a profit or loss. If so, wouldn't this assumption suffice for no arbitrage principle? Why are we specifically assuming a loss for St>K2?

If theres a loss for K1 < St < K2 then by the shape of the payoff there must also be a loss for St>K2. So St>K2 representing the lower part of the curve must be a loss at the very least.

 

[Joe Hook]

What about this one in April 2018, Q7 part iv)? Sorry, marked this as Q6 iv) originally.

Sorry yes I missed this one. The examiners obviously weren't looking for specifics here just the idea of beta based measures where it represents a subset of assets and a standard deviation based metric where it represents the whole portfolio. I certainly wouldn't mind seeing some specifics, so the actual measures you might use in both cases, it's just that the examiners didn't credit them here. Presumably because we've already calculated them above.

 

[Joe Hook]

Can you please elaborate? Does it mean that convenience yield is positive value currently but as futures are long term in nature, this convenience yield is not relevant? Hence, it is deducted.

Why is it relevant for only commodities not widely held as investment? Keen to know more about the practical aspect of this to make recalling this part easier.

The convenience yield is a positive value and puts a numerical value on having access to the asset in the short-term. As you say futures are longer term and so not subject to the same short-term supply issues. I'm not sure what you mean by "not widely held as investment". Convenience yields may apply to all futures but we only need to consider them for commodities for the purpose of SP5. Similarly, the exam is going to focus on the Core Reading. So your knowledge here need only extend to the formula for a commodities future and some simple statements about cost of carry and convenience yield.

So I wouldn't worry too much about recalling this information. You may want to make a simple flashcard if you do not have one already for this topic.

Joe

 

[1495_sc]

Inconsistent yes, but bear in mind that I constructed that situation without any allowance for premiums for simplicity. Once we factor in premiums then we should end up with some negative profits.

The Core Reading expects you to be able to construct option diagrams and diagrams for portfolios of options. This question tests your ability to take an portfolio diagram and identify it's constituent parts. So whilst you won't be asked to draw any diagrams (because the exam is in Word) a question such as this is a test of your ability to do so. So no rules of thumb here, just make sure you can draw payoffs and combine them together and this will help you identify any such profit shapes that come up in the exam.

Alright. Thank you!

 

[1495_sc]

Sorry yes I missed this one. The examiners obviously weren't looking for specifics here just the idea of beta based measures where it represents a subset of assets and a standard deviation based metric where it represents the whole portfolio. I certainly wouldn't mind seeing some specifics, so the actual measures you might use in both cases, it's just that the examiners didn't credit them here. Presumably because we've already calculated them above.

Ok thank you

 

[1495_sc]

The convenience yield is a positive value and puts a numerical value on having access to the asset in the short-term. As you say futures are longer term and so not subject to the same short-term supply issues. I'm not sure what you mean by "not widely held as investment". Convenience yields may apply to all futures but we only need to consider them for commodities for the purpose of SP5. Similarly, the exam is going to focus on the Core Reading. So your knowledge here need only extend to the formula for a commodities future and some simple statements about cost of carry and convenience yield.

So I wouldn't worry too much about recalling this information. You may want to make a simple flashcard if you do not have one already for this topic.

Joe

Sounds good now! Thank you

 

[1495_sc]

Few more questions, related to taxation and behavioral finance. Need help.

April 2012-Q5, ii)

In the question, for Country B's allowances, depreciating assets (includes automobiles) can offset 25% of value from any tax payable.

I interpreted this as ' If there are any depreciating assets, we can deduct 25% of the value of the asset from total tax payable and this holds true for automobiles'

Both investment and share portfolio have deteriorated from year 2 to year 3 and automobile collection has appreciated from year 2 to year 3.

However, investment and share portfolio have appreciated if we compare year 1 start value with year 3 end value.

The solution calculates tax for automobile as 15%*(1-0.25)*1500 for year 3. Although automobile is included in the definition of 'assets' in the question, it is not depreciating. Why are we offsetting via automobiles? Why not apply this logic for investment portfolio and share portfolio on the contrary as they are depreciating assets (When compared with year 2). I am confused.
Can someone please help?

October 2011, Q8

ii)1- Shouldn't this behavior be attributed to loss aversion theory? Manager is risk seeking when it comes to losses, hence she is holding on to underperforming stock.

Similar logic for April 2017, Q5 i)b) I thought of prospect theory here but the solution did not consider prospect theory. Where am I going wrong?

October 2012, Q3

ii) b) I thought of this as momentum effect where the individual assumes that the future will continue performing well in future. Or, representative heuristics/ availability bias. However, none of these theories are present in Examiner's report. My question is, why have we only considered anchoring and adjustment- ignoring all of the theories which I thought of!
This has happened many a times with theories of behavioral finance. Slightly worrisome.

Thank you!

 

[Joe Hook]

An unusual question on tax. I had to look long and hard at this one. I think the issue you are having (and I would probably have it as well) is the difference between depreciation and capital losses. The automobiles are the only assets that depreciate and so the increase in value of that section of the portfolio is presumably down to buying more automobiles. So by the tax rules of country B we can offset some of our tax by 25% of the value of automobiles after 3 years.

October 2011 - For part (ii) finding 1, I don't think it's clear enough that this is prospect theory as underperforming stocks do not necessarily imply loss (perhaps loss only relative to some benchmark) and it's also not clear that continuing to invest in the underperforming stocks is the riskiest strategy.

April 2017 Q5 - Again we could perhaps make the argument here that the investors are not necessarily making a loss, simply underperforming vs the benchmark. However, prospect theory does seem more reasonable in this case. Unfortunately with behavioural finance questions the examiners will generally award marks for a few of the most relevant points to the question and there are several more relevant biases we could include here.

October 2012 Q3 - I have some sympathy with you here. However, momentum is really behaviour at a market level and here we are considering an individual. Anchoring can be used in situations where our views are or opinions are based on past history as we have here. I think you could make an argument for availability...that the individual places a high probability of the value of the tulip futures increasing because they can picture this more vividly based on past information. The examiners report does comment that alternative solutions with appropriate explanation would be credited although unfortunately those alternatives are not stated so we cannot be sure what would score.

Behavioural finance questions can actually prove to be quite challenging because arguments can be made for quite a few for any situation presented. The examiners will show a little bit of flexibility in the answers they will accept but generally they will have worded the situation fairly specifically to try to get students to pick up on one or two. Make sure when answering such questions that you believe you've chosen the most relevant one or two behaviours. I suspect that you have done this in the questions highlighted above but perhaps you could go back and reflect on the question wording to see if there's anything there that would have pointed you towards another bias or behaviour.

Hope this helps.
Joe

 

[1495_sc]

Thank you for taking out time to answer my questions!

For the tax question, I understand the wording now. It was a generic statement talking about how any tax on depreciating assets can be used to offset losses.

Hope tax isn't so tricky in exam!

Will revise the behavioral finance theories to ensure I clearly understand what is more relevant when. Your note is very helpful. Thanks again.