Saturday, 16 November 2013

Equalising Formula

L commented on my past post about levelling up your profits (or losses) writing:

Nice stuff
Is possible to specify mechanically the risk reward ratio of bets in this case variable hedge? For example, at twice the rate sell 50% stake etc...
It is an easy calculation to determine how much you should lay to level up your position. Basically it is the difference between your green and your red, divided by the price, so if you are in the position I was in, Warriors -£600, Thunder +£2,300, Thunder price 1.6, the formula of (Difference) / Price tells you the amount to lay is £1,812.50.
Difference = £2,900 / 1.6 = £1,812.50. 
If you lay this amount, your red of £600 on the Warriors goes to a green £1,212.50, while your green on the Thunder reduces from £2,300 to £1,212.50.
It's easy to set up a simple spreadsheet to input your three variables, and output the amount to lay.

Ellis Rayner said:

If you believe 1.6 was a fair price then how about loading your greens to reflect that? 1.6 = 62.5% so based on your figures about £1,420 and £850
I'm not sure what Ellis is suggesting here by 'loading my greens'. Sounds like something my Mum used to do with my dinner. My What If? formula shows that laying £1,450 would leave a situation close to what Ellis suggests, but when you leave your outcomes significantly different with a fair (correct / true) price available, one is in second-guessing territory, which is a land I am trying to leave.


Ellis Rayner said...

If the 'fair (correct / true) price available' is 1.6 then you are saying that outcome has a 62.5% chance of winning. You can then adjust your position to reflect this % chance.

Not sure what's being second-guessed
if you are confident that 1.6 is the correct price?

fizzer555 said...

Cassini, In this example, I'm interested to know how you would approach it if the value price was still with the Thunder. If, for example, the Thunder price was 1.7 would you bet more on the Thunder because there was value in doing so or, because preserving your bank is important, would you stick with the +2300/-600 position given that, in your fair odds situation there was a 37.5% of losing. (I'm assuming the 3rd option of hedging or leveling up at bad odds is not a consideration because you are giving up value).

Emp said...

This issue is interesting to me because cricket (a sport built for in-play if ever there was one) presents this issue all the time.

I think a good general heuristic is to not add more at short prices to positions that are profitable (could be greened up) unless the position offers massive value. Also, consider that value assessments might be wrong and destructively so at short-prices. An example for those who follow cricket: many were slaughtered by India's effortless 359 run chase against Australia, though the half-time prices as short as they were looked to offer real value on Australia

I agree with Cassini about greening up. Theoretically maximizing EV should matter over bank preservation, but the latter allows you to build up more smoothly, not to mention that people aren't robots and very few can perform perfectly despite large set-backs and swings.

That said, sacrificing value to green up can be destructive and makes no long term sense, so I'd just let it run.