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There is a well known result that if you have to choose the best option from a set of randomly distributed options then you should sample the first 37% of them, then from the remaining 63% select the first option better than the best of the first 37%. This algorithm doesn't guarantee you have selected the best option, but it gives the best results when averaged over many runs.

With the start of the UK financial year imminent I have to choose when in the next financial year to invest in a stocks and shares ISA. Normally I just invest the maximum as soon as the financial year starts on the grounds that it's hard (impossible?) to game the system, and I'll probably do the same this year. However the stock market has reached a high just as the next financial year starts, and this made me wonder if it was worth waiting to see if the market goes down again.

I realise there is no way to guarantee you are investing at the optimal time, and I am not asking for advice as to when to invest. My question is whether there is any strategy akin to the 37% rule that gives you the best chance of investing at a good time in the next twelve months? Is this a problem that anyone has approached mathematically or statistically? It does not seem likely the 37% rule would apply since the 37% rule assumes that on average the value of the options remains constant, but on average the value of the stock market increases.

Somewhat belatedly I see there is a similar question: Investing in stocks & shares ISA- when to make deposits? To distinguish my question from the previous one let me clarify that I am not asking when I should invest. I am asking whether there are any studies of the optimal strategy in these circumstances?

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  • So the idea is to invest the first time it goes below the lowest point in your 37% (or else at the end of the year)?
    – Paŭlo Ebermann
    Commented Apr 5 at 0:10
  • The secretary problem is not a good way of looking at this as it gives a 63% probability you will not invest at all. Since the purpose of the ISA wrapper is to avoid income tax and capital gains tax on a given investment made in a tax year, the cost of not investing if you have the money available would be bigger than trying to time the market.
    – Henry
    Commented Apr 5 at 10:07

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If you Google "lump sum vs. drip feed" you will find lots of analysis of the topic of scheduling investments (for example https://monevator.com/lump-sum-investing-versus-drip-feeding/ ). Short story is that if you believe markets generally go up and that they're efficient, then statistically the best thing to do is to go all-in as soon as you can, to get all of the value of your cash working for as long as possible, and that link cites studies showing this working in practice. However there may be harder to quantify psychological feel-good advantages to drip feeding, and if those help you stay invested rather than bugging out and selling low in a crash, then that might translate into superior returns in the long run.

An investing approach similar to the "secretary problem" solution might be the common "moving average" one, where comparing stock prices or index values to the average value over the last (typically) 50 or 200 days is used to form some opinion on the future direction of travel. Perhaps surprisingly, most of what you read about it involves buying stocks above their recent-history average on the grounds they're on a "bull run" (so-called "trend following" or "momentum trading") rather than buying ones below it (in the hope "oversold" stocks will experience a "reversion to mean" recovery). A good read on this at https://monevator.com/trend-following-is-the-trend-your-friend/

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    Thanks :-) I guess the key point is that on average the index rises so on average the biggest gain comes from investing as early as possible. The situation is actually pretty straightforward. It turns out I have been (unknowingly!) following the optimal strategy.
    – John Rennie
    Commented Apr 5 at 5:26
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The popular phrase is "time in the market beats timing the market". You can't know what the market is going to do next, and the quicker you invest, the more time your investment will have to grow.

There's also the advantage that most forms of taxes and savings are taxable, bit an ISA isn't. So if you leave your money outside an ISA, waiting for the right time to invest, you may get taxed on any returns you make in the meantime.

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  • Time in the market, over what time horizon, 5 yrs, 50 yrs, 500 yrs?
    – paulj
    Commented Apr 5 at 11:49
  • @paulj Any medium-to-long time period. Growth is compounding. So if you invest now, rather than in 6 months' time, then that extra 6 months of growth will keep compounding for all the time you have the investment.
    – Simon B
    Commented Apr 5 at 19:40

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