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Long Volatility as an Investment

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1. since when has the market averaged 10% compounded growth excluding dividends? Especially over a life time as in Wayne’s example.

2. and as I said at the moment some stocks “insurance premiums” are selling for over 18%, so at that price even your 10% growth factor is dwarfed by the Premiums you are paying out.

3. I don’t think picking up annualised premiums of 18% of the insured value is the same as “picking up pennies”

—————
as for insuring an increasing capital base it works both ways.

4. the capital base would have to drop 18% in the first year to break even, if it only dropped 10% you lost, and the insurance in the second year would be based on the lower capital base.

1.



2. But as already indicated, your example isn't what the thread is actually discussing. You have missed the point. So let's take a real example from today's prices:



So you are selling a PUT just OTM at strike $353.00

The following applies:





4. Incorrect.

So you will pocket $9.30.

The market falls 10%



$35.49 - $9.30 = (-$26.19). You have just lost x3 your money. A real outlier, oh, 2020 and 30%...



Now your loss is (-$96.77). That is x10 your money. See how declines are not proportional to your losses?

3. I do.

Now that is an index. Do that on individual stocks, which are more volatile than an index and your are playing with a significant amount of risk, seemingly without really understanding what you are actually doing.

jog on
duc
 
@Value Collector So long as the gamma monster doesn't catch you.

To repeat once again, the same beast that ate LCTM.

But that's off topic, the topic here is *long volatility* as a strategic aspect of a total portfolio.

Long theta/short gamma is a whole 'nuther bowl of wax.
 
... short gamma is also what ate Nick "the wonder boy" Leeson and bankrupted Barrings Bank.

As such, it is absolutely antithetical to the topic at hand.
 

Ok, you are confused.

That table that you put up showing a 9.43% return since 1982, includes dividends of about 6% which as I said those dividends would have been spent on premiums, the 12.09% is reinvesting and compounding those dividends, So like I said the capital gain excluding dividends is much lower than 10%.

Secondly when I said some shares cost over 18% to insure I was talking about FMG, as of 11am today the market is as follows

FMG share price $16.81,.... Cost for a $16.50 Jan put option = circa 82 cents, thats for 2 months protection, so if you were selling that put every 2 months that would cost you $4.92 for the year, thats about 30% of the insured value paid as premiums over the year, even if you bought 6 moths cover you are still paying 20%+ as premiums, and that for out of the money options

That is why I said when insurance is so expensive, I much prefer to be selling insurance rather than buying it, good luck hoping to out run insurance premiums of 30% or 18% by capital gains over time, hell unless the drop is fairly sudden the premiums collected are likely to dwalf any permanent drop in the future,.
 
Ok, you are confused.

1. That table that you put up showing a 9.43% return since 1982, includes dividends of about 6% which as I said those dividends would have been spent on premiums, the 12.09% is reinvesting and compounding those dividends, So like I said the capital gain excluding dividends is much lower than 10%.

2. Secondly when I said some shares cost over 18% to insure I was talking about FMG, as of 11am today the market is as follows

3. FMG share price $16.81,.... Cost for a $16.50 Jan put option = circa 82 cents, thats for 2 months protection, so if you were selling that put every 2 months that would cost you $4.92 for the year, thats about 30% of the insured value paid as premiums over the year, even if you bought 6 moths cover you are still paying 20%+ as premiums, and that for out of the money options

4. That is why I said when insurance is so expensive, I much prefer to be selling insurance rather than buying it, good luck hoping to out run insurance premiums of 30% or 18% by capital gains over time, hell unless the drop is fairly sudden the premiums collected are likely to dwalf any permanent drop in the future,.

1. That table is merely to demonstrate that circa 10% (excluding dividends) was available. You doubted that 10% was available. That of course is an index of 500 stocks.

2. Let's stick with your FMG, even though it has nothing to do with the issue in this thread. So:



And the chart:



A possible (lower) price: $12



So for your $0.87 premium, you lose $3.78.

4. Aren't all drops sudden?

jog on
duc
 
ducati916 said:
$35.49 - $9.30 = (-$26.19). You have just lost x3 your money. A real outlier, oh, 2020 and 30%...

Now your loss is (-$96.77). That is x10 your money. See how declines are not proportional to your losses?
Click to expand...

that's all true, but that's only evaluating a single month in isolation, the strategy has to be evaluated over the longer timeframe. it's a bit of a stretch to selectively pick and choose which months you'll buy protection and which months you won't, because you don't reliably know in advance which month the 10% blowup will occur in, nobody does. you don't insure your house just for January and leave it uninsured the rest of the year. and if you adopt the approach of waiting for signs of a potential blowup before taking out the protection, the IVs will have already risen by then making the premiums drastically more expensive.

if the blowup happens a year into the strategy, assuming constant vols the put seller will have already collected $93 in premiums, minus whatever is lost in the months where the options only expire slightly ITM. there's a decent chance that's going to be more than $35.49.

even if the blowup happens in the first month, the put seller is temporarily down $26.19, but if sufficiently collateralised so that one month doesn't knock them out, they can make it back over the coming months, as the market just does not fall by 10% a month for several months in quick succession, in the same way that you don't have disasters requiring you to claim on your home insurance month after month (if you do, i'd suggest maybe moving somewhere else?)
 
ducati916 said:
So for your $0.87 premium, you lose $3.78.

4. Aren't all drops sudden?

jog on
duc
Click to expand...

There is only 2 months until the Jan contracts expire, not 3.

and as Sharkman pointed out, you selectively assuming this sudden drop happens within the first 2 month period, which's I said if it happened would result in a good speculative gain, but as longterm strategy, paying 30% per year of an assets capital value is probably no going to be wise, because you are counting on a shorter sudden drop, if that doesn't happen you will be bleeding capital.

I will happily sell you insurance on FMG stock at $16.50 for 40 cents per share each month for the rest of your life if you think its a great deal, I would suddenly have a great little synthetic FMG portfolio paying $4.80 in dividends per year, that a synthetic 29% dividend yield for me, and I didn't even have to buy any shares.

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In my opinion you should ditch the black and Scholes formula, Beta doesn't give you any real guide to actual longterm risk, crunch the data of the actual companies from a business perspective, and you find gems like FMG currently is where the options prices way over valued compared to the actual business risk involved, which allows a long term play with patient capital to profit from the markets mis pricing.
 
The point may be missed that the allegory of the Hawk and The serpent and the dragon portfolio he's meant to be a lifetime portfolio.

Talking about the expense or not of insurance at any one particular point in time it's not relevant in the timeframe being considered. As mentioned several times now by both myself and The Ductser, in the context of this thread it is off topic.

But in the context a discussion as it has progressed, let look at ratio spreads, which is one of the ways in which is proposed for being strategically long volatility.

Reverse ratio put spread as proposed, is put on at all near zero cost (notwithstanding SPAN requirements for the long put risk at expiry). This is at the cost near term -Delta. However in our corner fighting for us if and when the market blows the f*** up, is positive gamma.

We can dodge the substantive portion of -theta in the valley of the shadow of death I using long dated options which maximizes our vega anyway.... That's what we want.

We can roll the spread as appropriate well before expiry so the decay is ameliorated, if the market is hovering around that strike.

Now let's turn the whole thing around and do the mirror image, ie -gamma ratio spread.

Ya still wanna play?

Not this little black duck, that is for sure. The apostle Taleb would be pulling what remains of his hair out at the mere thought of it and brother Cole it would be walking away, shaking his head, and muttering to himself.

If you want to play the short options game, that is completely fine but it is a whole different thesis and a whole different approach on a whole different time frame.

I'm not averse to throwing my hat in that particular ring at times, but as an ad nauseam reiteration, that is not the topic thread.

If I'm sure options I want to be on top of the market all the freaking time, so if the barbarians are at the gate I can bid a hasty retreat with the minimum of damage.

In a dragon portfolio of which long volatility is a portion thereof, the idea is to be able to do a little fishing in the morning, make siesta with the missus and play a guitar while drinking beer with my mates in the afternoon... With just a little tweaking up the portfolio here and there every few weeks.... or months. (Bonus points for the allegorical reference).
 
wayneL said:
Now let's turn the whole thing around and do the mirror image, ie -gamma ratio spread.

Ya still wanna play?
Click to expand...

you're referring to a ratio put front spread i take it, eg. buy 1 ATM put, sell 2 OTM puts, same expiry? sure, i do 'em fairly regularly. got one on BHP (36.50-35 for 0.18 credit, expiring next week) right now. different strats appeal to different people/objectives. but ok, happy to set aside the short gamma stuff for another time/topic and focus on the put back spreads. though i can't offer much in the way of discussion on that (and whatever i say is liable to be wrong) as i'm very inexperienced in this area - i've done maybe 2 or 3 of those lifetime. but definitely interested in delving into some details, maybe with some hypothetical trades (with realistic market data) if anyone's keen.

so from my limited understanding of the put back spread, it does cover tail risk better, but as far as i can tell, the market already knows this/factors it in, and 99.9% of the time it will charge a hefty IV when buying say 25d puts, vs ATM where you're selling a leg at least a few vol lower, making it harder to put this on for small credit or at least zero cost (which i imagine is what we're striving for here).

if you go further out in time, then you have to widen the distance between the strikes to keep it relatively close to zero cost, thus increasing the width of that dead zone where you take losses on a moderate fall. if the lower strike is too close to ATM, negative theta would be almost unavoidable? maybe turning it into a diagonal where the quicker decay of the front month sold ATM better counteracts the negative theta of the larger number of bought back month OTMs could be an alternative, but that has its own risks.

from memory, the few times i traded this, i ran into the same sort of difficulty as cutz mentioned, it drops to that dead zone around the lower strike and gets stuck there. you're paying a truckload of decay at that point. how would one go about managing the position then - what sort of factors eg. time to expiry would be taken into consideration when looking to roll, letting it play out a bit more etc.

choice of strikes would be an important consideration too i'd imagine, and possibly that's where i went wrong in my earlier attempts at this strategy. a few alternatives just thinking off the top of my head here:

- sell ATM, then buy twice as many OTMs at the highest strike that will get the whole structure to zero cost?
- line up the lower strike with some perceived support level? then sell half as many of the upper strike at whatever strike gets it close to zero cost? or sell the upper strike at ATM and adjust the ratio instead to get it to zero cost?
- line up the lower breakeven with that support level?

probably many other possibilities there. what would everyone else take into consideration when selecting the strikes/ratio used for such a strategy?
 

Pre Covid it was possible to do a 1:2 for a credit (XJOs 300 wide ) depending on strike selection, haven't done these in a while having a preference for iron flys with adjustments, the recent meltdown left me shaken, this week after closing out front short puts best compromise for me at approx 60 DTE, a 2:3 ratio, high sixties credit with some meltdown protection.

The call side is still a work in progress.
 
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1. that's all true, but that's only evaluating a single month in isolation, the strategy has to be evaluated over the longer timeframe. it's a bit of a stretch to selectively pick and choose which months you'll buy protection and which months you won't, because you don't reliably know in advance which month the 10% blowup will occur in, nobody does. you don't insure your house just for January and leave it uninsured the rest of the year. and if you adopt the approach of waiting for signs of a potential blowup before taking out the protection, the IVs will have already risen by then making the premiums drastically more expensive.

2. if the blowup happens a year into the strategy, assuming constant vols the put seller will have already collected $93 in premiums, minus whatever is lost in the months where the options only expire slightly ITM. there's a decent chance that's going to be more than $35.49.

3. even if the blowup happens in the first month, the put seller is temporarily down $26.19, but if sufficiently collateralised so that one month doesn't knock them out, they can make it back over the coming months, as the market just does not fall by 10% a month for several months in quick succession, in the same way that you don't have disasters requiring you to claim on your home insurance month after month (if you do, i'd suggest maybe moving somewhere else?)



Mr Sharkman:

1. That $4.92 is 1 years worth of premiums (if we are talking about FMG). All it takes is 1 decline of that magnitude, 28% and the entire year's premiums vanish. Through the year (see chart) there were any number of falls of a magnitude that are going to cause losses. I count 3 significant falls and another 2/3 lesser falls. As Taleb said: Where all swan's are considered white, you only need 1 sighting of a black swan to disprove the assertion (hypothesis) that all swans are white.

2. Right so now you are referring to SPY. (a) you can't assume constant vols. as vols. constantly vary, (b) there have been more than 1 instance this year of falls that would cause losses significant enough to invalidate the strategy: 1 major, x2 over 10% and a number of lesser declines. On the SPY this is a losing strategy the way VC advocates.

3. If it happened in the first 3 months (which it did) and you were selling 1/month, you will be down huge, as there was a 40% decline. You would never have seen the rest of the year, as you would have been carried out on your shield.


Mr VC said:

1. There is only 2 months until the Jan contracts expire, not 3.

2. and as Sharkman pointed out, you selectively assuming this sudden drop happens within the first 2 month period, which's I said if it happened would result in a good speculative gain, but as longterm strategy, paying 30% per year of an assets capital value is probably no going to be wise, because you are counting on a shorter sudden drop, if that doesn't happen you will be bleeding capital.

3. I will happily sell you insurance on FMG stock at $16.50 for 40 cents per share each month for the rest of your life if you think its a great deal, I would suddenly have a great little synthetic FMG portfolio paying $4.80 in dividends per year, that a synthetic 29% dividend yield for me, and I didn't even have to buy any shares.

------------
4. (a) In my opinion you should ditch the black and Scholes formula,

(b) Beta doesn't give you any real guide to actual longterm risk,

(c) crunch the data of the actual companies from a business perspective, and you find gems like FMG currently is where the options prices way over valued compared to the actual business risk involved, which allows a long term play with patient capital to profit from the markets mis pricing.



1. Immaterial.

2. It makes no difference 'when' it happens if it happens. Secondly, there was more than just the 1 fall in reality. Your strategy entails risk that you are seemingly unaware of.

3. I'm sure you would.

4. (a) Do you have any actual data or an argued position (reason) that Black Scholes should be ditched other than your opinion? I'm perfectly aware of some of its shortcomings, are you? If so, clarify your criticism and provide some value, rather than simply the empty 'in my opinion' which tells me nothing.

(b) The only way you live to see the 'longterm' is surviving the short term. It has already been demonstrated that there is a high probability that you would not survive the short term, in the way you have argued your position.

(c) We have already been down that avenue: https://www.aussiestockforums.com/threads/the-education-of-an-investor.34402/page-16, you missed blatant financial statement fraud.

jog on
duc
 

I am not sure what your concept of “long term” is, but I have 8 years of profitable options trading under my belt now, with zero years of loss, and this year is by far the most profitable.

And I have never once used the black and scholes formula, to be honest I couldn’t even tell you what the Greeks “gamma” and “delta” are, they are actually entirely irrelevant to my strategy.

My strategy is based on Manuel underwriting based on company fundamentals / business valuations, and writing conservative levels of insurance against a small number of companies that I understand from a business perspective through the cycle.

if understand a company, and are operating from a business / underwriting perspective, the black and scholes formula is not required.

In my opinion the black and scholes formula is a short cut technique for those that want to avoid doing the leg work of Manuel valuation and underwriting, it substitutes the “real risk” with “volatility”,when in reality risk and volatility are not the same thing.

infact I think I have profitably taken advantage of the system by identifying situations where volatility is high, but actual long term risk is low which as in the FMG example allows me to sell insurance for much higher prices than is warranted.

immaterial
Click to expand...

collecting 6 premiums a year vs 4 is not immaterial.
 
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Also Duc,

If you reply can you use the actual reply button, they way you are doing it means I don’t get a notification, and the layout of your replies is also very confusing.
 
I think we're getting a little bit off on a tangent with regards to time horizons here. Cole model his portfolio thesis based on the last 100 years of data to try and find a superior way to have the very long-term portfolio strategy rather than the standard 60/40 stocks and bonds.

This is no trading strategy and in no way resembles constantly selling premium. As I said several times already that is a whole different ball game in its own right, hence to points The Ducster is making above.

@Value Collector have you actually read the Allegory of The Hawk and The Serpent?

The outline is here as well as a link to the PDF of his original paper. This will explain the particular philosophical approach to that portion of his proposed portfolio that is volatility as strategic investment so we don't get further waylaid off on this strategy is better or that strategy is better. The idea is to discuss ways of doing this.

Welcome — Artemis

www.artemiscm.com

Th intention here was to discuss the ways that one could construct long volatility in portfolio. There are various ways, long puts is one way reverse ratio spreads are another way.

On can even discuss the use of VIX futs)ETFs and other options strategies (or not as the case may be), that what I was trying to discuss here.
 

Over the latest 100 years, you would have been better just owning 100% stocks, no bonds and no hedging, provided you have the stomach muscles to accept the ups and downs.

Maybe you guys know of free ways to hedge against volatility, I don't know of cost free hedging, as far as I can see hedging always costs something, and it general it would be better over time to take that risk on your own balance sheet.
 
1. I am not sure what your concept of “long term” is, but I have 8 years of profitable options trading under my belt now, with zero years of loss, and this year is by far the most profitable.

2. And I have never once used the black and scholes formula, to be honest I couldn’t even tell you what the Greeks “gamma” and “delta” are, they are actually entirely irrelevant to my strategy.

3. My strategy is based on Manuel underwriting based on company fundamentals / business valuations, and writing conservative levels of insurance against a small number of companies that I understand from a business perspective through the cycle.

4. if understand a company, and are operating from a business / underwriting perspective, the black and scholes formula is not required.

5. In my opinion the black and scholes formula is a short cut technique for those that want to avoid doing the leg work of Manuel valuation and underwriting,

5.(a) it substitutes the “real risk” with “volatility”,when in reality risk and volatility are not the same thing.

6. infact I think I have profitably taken advantage of the system by identifying situations where volatility is high, but actual long term risk is low which as in the FMG example allows me to sell insurance for much higher prices than is warranted.



7. collecting 6 premiums a year vs 4 is not immaterial.



1. I could write a long list of those that have blown themselves up, but the one closest to your heart would probably be Ben Graham. 8yrs is nothing, a blink of an eye. Your argument is that the past is a fair predictor of the future. In some walks of life, that may be a fair assumption. In the markets, it is not.

2. So your assessment of the tool is based upon zero application of it. Does that not rather suggest that your mind is closed?

3. Which as far as it goes, is fine. However you have inserted into that strategy, the use (abuse) of derivatives. We have (12 yrs ago, outside of your current range of experience) had the financial system almost topple due to derivatives and the so called Masters of the Universe blowing themselves up. Buffett himself suffered significant losses on a purchase, due to derivative exposure that he failed to correctly calculate his exposure on (the fundamentals are affected by derivatives). Since you now drive a TSLA, I'm guessing you may have forgotten, playing with petrol next to a bonfire is dangerous.

4. But as you have never used the B/S model, don't understand its inputs and outputs, that is simply an uneducated position to take. Second, what you are trading is a derivative, which while linked to your 'business', will not (necessarily) due to the leverage, reflect even approximately any fundamental value you have calculated.

5. All I see is the evidence, provided by yourself that you are too lazy to investigate whether the B/S has any value to add to your positions. Your opinion as to whether others are lazy/etc, is simply an unsubstantiated opinion, a bias, a prejudice.

5(a) You don't even seem to understand your own arguments: if your argument is that volatility and risk of common stocks are uncorrelated, that is a position argued by long term buy and hold investors, essentially I agree. However if you are a day trader trading common stocks, that statement is false: volatility and risk are highly correlated in common stocks.

However, that is not even the issue: your position is that volatility and risk are not correlated in OPTIONS. That is simply incorrect. Of all the variables that create the price of an Option (Time, Price, Volatility, Interest Rates, Strike Price Dividend yield) volatility has possibly the most significant impact of all.

6. If you 'think', then you are only guessing. If you knew, you could provide all the data of the trade and demonstrate exactly why it is a good trade or even a great trade. Even with all of that, it can still go wrong, but, you will know exactly why/when it has gone south and the correct response to that change. You have no idea.

7. If your total collection of premium is $4.96 (whatever) then explain to me why it is material that you collect it over 6 periods rather than 4 or any number that you choose.

This is really for whoever is interested. It is a thread from a British forum on exactly this topic, selling Options premium, by a chap who thought he was just a little special: https://www.trade2win.com/threads/plain-vanilla-options-trades.23221/

@wayneL, you will enjoy this one!

jog on
duc
 

I am still not sure why you are not clicking the reply button, and structuring your replies in this way but.

1, I have been investing for 24 years, I added options as an extension of my strategy 8 years ago, I made a lot of money in the GFC, so yes that bit of history I have Experianced.

2, my mind isn’t closed about the Black Scholes formula, I studied it quite a bit when I was first learning about options, I have just decided that it isn’t necessary, and that a manual valuation is more accurate, as I said Beta doesn’t tell you about risk, it’s a short cut at best.

3, how am I abusing derivatives?

4, if I calculate that XYZ company is worth $4 per share, and would be happy to add it to my portfolio at that price, and some one wants to pay me $0.10 every 3 months for an option to sell me their stock at $3.50, I don’t need the B/S formula to tell me that that’s a great deal, I can earn an 11% return on my notional XYZ shares until they drop and I have to take delivery, that not “abuse of derivatives” that’s sound underwriting.

5, I am not a day trader, I am a long term investor in the process of accumulating an ever larger amount of stock, selling puts is just part of that strategy, think of it like have a buy order open that I get paid for have open, where I base the prices I accept are based on my manual valuations rather than B/S formula.

6. don’t get hung up on the word “think”, it’s just a figure of speech, I am far more likely to use words like “I believe” or “I think” than “I know” especially when something is kind of unknowable or based on estimates such as valuing a company or assessing risk, it’s easy to know the beta of a stock, it’s harder to know the actual real world risk, that’s why they chose to use the beta in the B/S formula because it’s easy, but knowing the precise beta doesn’t give you an edge over someone who has an understanding of approximate real world risk, who was it that said it’s best to be approximately right rather than precisely wrong?

7. because we were talking about earning $X amount per contract, 6 contracts is more than 4 contracts, eg if I said I was going to pay you $10,000 every 2 months, you would earn more than if I paid you $10,000 every 3 months.
 
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1. Ok, on that basis then you will accept that certain businesses (common stocks) were bankrupted and liquidated during that period, 2 of the more famous examples being Bear Stearns and Lehman's. A risk when investing in financial markets is that the business fails.

2. Now you say you have studied it extensively, in your prior post you said:



The lack of a consistent position is concerning.


[4] and [5] because this is the issue:

(a) You are valuing a common stock at (in your example) $4/share. You are selling a PUT at Strike $3.50 and will take delivery in a price decline. In your eyes you are buying at a $0.50/share discount, ignoring the price decline (beta) as short term and irrelevant.

(b) This allows you to ignore the losses on the Option, because you will take delivery. There are no margin calls as you will have the cash to take delivery of the shares.

(c) The 'risk' is that your valuation is wrong and/or that business is liquidated. Your loss on that entire transaction is now 100%.

This strategy is not 'selling insurance', when you sell insurance, you indemnify the buyer against loss. Insurance is sold to someone. You are selling a PUT that you intend to use yourself. That is not selling insurance. Your incorrect use of terms has created the confusion on this thread.

This is definitely not what @wayneL is referring to. This is a strategy that value chaps play to try and boost returns because they have uninvested capital. As such it's not right or wrong, but it is totally irrelevant to this thread.

6. The word 'think' is the correct word to use because, you don't know. Which is exactly why I posted:



7. This is basic error.





No we are talking about earning $4.96 in sold premium in TOTAL. Therefore if the maximum you can earn is $4.96 you would actually be better off earning it all at once and being able to sell for the total premium in 1 transaction.

As for [3] that is rather self-explanatory.

jog on
duc
 

1. yes, companies went bankrupt and the Beta of their stock didn’t give any idea of the risk for the years and months leading up to that, however if you have seen the movie the Big short, you will see guys that did Manuel valuations of the underlying bonds etc figured out what was happening and profited from it.

2. Yes 8 years ago when I first started researching options I read quite a bit about about the BS formula, but yes now I couldn’t tell the what delta or gamma are, I have data dumped that because I don’t use it.

B, what losses on the options I take delivery of? I hardly think taking delivery of FMG at $5 has caused any losses, but when I do take delivery of stock, the difference between the market price and the price I paid is recorded as a loss against my options income, and the market price is recorded as my cost price for those shares I hold long term, so no I am not ignoring any losses, I know my profit and loss to the cent.

c. Obviously, but that is the same for anyone that buys stock, either out right or using put options, what’s your point?

I am not sure you understand put contracts, they are a perfect example of selling insurance, you paragraph about them not being insurance doesn’t make sense at all, when I sell you a put contract, it is indemnifying you against the drop in price of the asset named in the put option contract, I am guaranteeing you I will buy it for a certain price with in a certain time.

6. yes it is the correct word to use, that’s why I used it, because as I said we are dealing In Things that are unknowable and can only be estimated, just because you say you “know” doesn’t mean you do, saying “I think”shows humility not ignorance in fact claiming to know the unknowable is arrogance and ignorance.

7. No, if you go back to the start I was describing earning $X on a certain contract and then multiplying that by 6 to get the annual rate, but then in your example you used that $x figure for 3 months which if you extrapolated that would have given you a wrong annual figure, hence why I said it’s a 2 month contract, but we are last that example now so who cares.
 
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