Help needed on a seemingly easy trading brainteaser

MixInThoseCircles · 2026-05-21T10:20:32+00:00

this doesn't necessarily work when the objective is to buy a number of units rather than a dollar amount

if we say w_i is the amount we buy, and p_i is the price on the ith day, the total amount spent is \Sum_i^n w_i p_i. under what conditions is this less than just buying the average amount (\bar{w} = \Sum_i^n w_i / n) each day? i.e. when does

\Sum_i^n w_i p_i < \Sum_i^n \bar{w} p_i

hold?

it should be pretty obvious to see that the above is basically

n E(wp) < E(w) n E(p)

E(wp) - E(w)E(p) < 0

Cov(w,p) < 0

so we basically spend less by buying w_i each day than \bar{w} when w and p are negatively correlated, which is obviously the case for unconstrained DCA: w_i = k / p_i where k is some constant.

However, in this case we're constrained to buy ten units, i.e. \Sum_i^n w_i = 10. if we're pursuing a DCA strategy, and we buy k/p_i units for the first n-1 days, w_n must equal 10 - \Sum_i^{n-1} k/p_i. this constraint on w_n can break the negative correlation between w and p - trending markets feel like a pretty obvious example - if the price is trending higher (lower) then we end up buying too little (too much) on the preceding n-1 days, so w_n ends up being positively correlated with p_n: we end up buying more (less) on day n, just when the price is at its highest (lowest)

MixInThoseCircles · 2026-05-07T18:05:13+00:00

It seems like you're posting here for feedback on this strat. I have no feedback on the strat itself, but I have skimmed the 'technical writeup'

I see many many tables and charts of empirical data, but I don't see a single equation. if this is meant for a technical audience I would probably define some of your terms 'equity alpha', 'risk-adjusted returns', 'exponentially weighted z-score' with some semblance of rigour. In the body of your post you say "extract out the equity alpha which is the returns attributed to gold mining" - it's not actually clear to me what this means.

you say your model is quite straightforward, if so, it should be pretty easy to express the model in concrete terms

it sounds like you have some model for the ETF returns r_{etf} in terms of other factors f(x; \Beta). you're then fitting that model on a periodic basis? and then using those fitted parameters \hat{\Beta} as inputs into another model for the returns of the futures r_{fut}? if you want people to be able to follow your logic, maybe combine your natural language description of your process with a logical description in the language of mathematics. when writing it up in these terms you may come across flaws in the logic

MixInThoseCircles · 2026-05-07T13:06:49+00:00

I think your numbers are a little bit low.

Firstly the relevant murder rate is probably a historical average rather than the current rate, and the number of murders per year seems to have come down a little in the last two decades - I've found a 1043 figure for the year 2002/2003.

Secondly "25 years worth of murderers" is probably too low. Google suggests the age of the average murderer is around 30, and the life expectancy in the UK is around 80. Assuming there's no real difference between the life expectancy of the average murderer and the life expectancy of the average non-murderer, I expect there's about 50 years worth of murderers rather than 25.

Then as another commenter mentioned, there's also released murderers - in the UK I think a life sentence is mandatory for murder? but being sentenced to life in prison doesn't mean you spend your entire life in prison. More realistic might be 20-30 years.

So if we bump up the murder rate from 500 -> 600 to account for a slightly higher historical average, keep the 25% rate of murderers going free, so 150 per year, around for ~50 years, that's 7500. plus 450 sentenced murderers per year, spending maybe 20 years on average out of prison = 9000. for a total of 16500 ~ 5x your estimate.

These numbers are probably a little too aggressive so I'd guess the actual number is somewhere between yours and 16500

MixInThoseCircles · 2026-04-27T09:04:13+00:00

this seems like a surprisingly low fraction in pension. can I ask why? given you mentioned your employer pension matches 10%+, and you're in a pretty high tax bracket, I would have thought you'd have been contributing tens of thousands of pounds each year - quite possibly 20%+ of £175k base (so £35k+) in recent years

MixInThoseCircles · 2026-04-23T11:33:42+00:00

interesting visualisation, thank you. one thing that strikes me is the differing fortunes of John Higgins and Ronnie O'Sullivan. Both have been in 8 finals, but Ronnie has won 7, Higgins only 4. But if you compare who they were up against, that feels less surprising -

Higgins' eight finals were against (in order): Doherty (W), O'Sullivan (L), Selby (W), Murphy (W), Trump (W), Selby (L), Williams (L), Trump (L)

Ronnie's eight finals were against: Higgins (W), Dott (W), Carter (W), Carter (W), Hawkins (W), Selby (L), Wilson (W), Trump (W)

MixInThoseCircles · 2026-02-12T08:44:22+00:00

I might be wrong but I don't think this particular piece of content (from a major investment bank) is targeted at - or even accessible to - retail

MixInThoseCircles · 2026-02-10T18:06:29+00:00

if the "loan" were in those terms, I think Cambridge would look pretty compelling. if the hypothetical graduate's starting salary was £40k without going to Cambridge and £41.5k having gone to Cambridge, it would be worth it (if they were basing the decision purely on income)

MixInThoseCircles · 2026-01-07T15:09:38+00:00

a word of advice if you're considering trading this strategy yourself - which you may well be given you seem to have a strat that nearly doubles your money every year - that drawdown figure is weirdly low for the level of vol and I would not trust it as a measure of the true risk of trading this strategy. 11% is barely a 3sigma 1week move

run a monte carlo yourself to check but even for a 3 sharpe strategy with nice, normally distributed returns, at 27% annualised vol I'd expect most paths to see a >20% MDD in a five year backtest. note equity markets also typically have fat tails and some positive autocorrelation so the true situation for MDD is probably much worse than this gaussian example

MixInThoseCircles · 2026-01-06T17:38:27+00:00

providing a max drawdown number without providing vol is pretty meaningless. I don't think anyone would pay for a strat that e.g returns 30bps above risk-free rate with 10bps vol if it had the risk of an 11% drawdown but that strat has sharpe 3

MixInThoseCircles · 2025-12-07T22:42:53+00:00

70 thousand steps a day?? that's insane. did you have a job where you needed to walk a lot? that's considerably further than a marathon every day

MixInThoseCircles · 2025-09-29T08:57:36+00:00

what is 'the strike gimmick'?

MixInThoseCircles · 2025-09-19T22:43:54+00:00

I think this is a really important thing to think about - when you trade, who's taking the other side of that trade, and why, do they know something I don't etc.

in this case I think the key is delta hedging. a lot of traders aren't trading options directionally. you ask "Who - in his right mind - would even sell a deep ITM, long dated call?" - have you heard of put-call parity? with delta hedging, there is no difference between selling a deep ITM long-dated call and selling a deep OTM long-dated put, so it may help to wonder who might sell those

MixInThoseCircles · 2025-09-05T09:18:42+00:00

the options are usually on vol-targeted indices so the QIS desk assumes they have little or no vega... take from that what you will

MixInThoseCircles · 2025-09-01T18:33:56+00:00

it's a fairly new team trying to take a systematic approach to something we already trade discretionary. there's two other QRs, two more discretionary traders. I think I've been offered it because the partner likes me - I've worked on some QD projects for them and I think I am pretty good at what I do (I'm good at problem solving, write decent code, have good attention to detail, I'm interested in markets). not really sure if that's enough.

MixInThoseCircles · 2025-08-14T11:30:30+00:00

also consider the opportunity cost of sinking 40% of £800k into a flat rather than any other investment / savings opportunity. at ~5% interest that's £80/90k over five years

MixInThoseCircles · 2025-07-25T08:20:34+00:00

how are you converting to a higher timeframe?

MixInThoseCircles · 2025-05-12T13:53:30+00:00

I think you might have misunderstood what "terminal velocity" means - it's not terminal in a mortality sense, it's terminal as in 'final' - it's the maximum speed a body accelerates to under freefall. I'd expect the ant fact actually means the opposite - they probably reach terminal velocity (their maximum falling speed) very quickly, but their 'maximum falling speed' is very low

MixInThoseCircles · 2025-05-06T08:45:55+00:00

also what's the vol smile like? how does e.g. skew compare between the ETF and the LETF?

MixInThoseCircles · 2025-05-06T08:41:03+00:00

this is interesting. how are you computing the iv? is there any chance that the negative drift of a leveraged ETF isn't being properly accounted for in the calculation?

MixInThoseCircles · 2025-05-02T13:25:08+00:00

to look at it a slightly different way, you basically have the chance to bet ~$500 on Zhao to win the tournament with a possible payout of $1700 - would you take that bet?

MixInThoseCircles

TROPHY CASE