6 ms·

Yes, lump sum maximises expected returns, but you typically don't want to just maximise expected returns. Volatility matters. If I give you this once in a life

by 317070 3y ago

Yes, lump sum maximises expected returns, but you typically don't want to just maximise expected returns. Volatility matters. If I give you this once in a lifetime trade: 100k for a 1 in a 1000 chance to win 500M, would you take it? There are very few people who would, even though it has 400k of expected returns, a whopping 400%. Most of us simply don't make enough money in a life to take that trade enough times to cope with its volatility. Elon Musk should probably take that trade though.

lordentropy 3y ago
If you have a long time horizon and invest in a broad-based index fund, why do you even care about short term volatility? If you need to withdraw money within the next few years, then yes volatility matters. But in that case, you might be better off not investing in stocks and go with less risky stuff.
- steveBK123 3y ago
  Everyone has a different definitions of short & long term, and the resulting volatility appetite. Volatility is also a lot easier to read and pontificate about than to experience in real time. What people do during draw downs is often emotion driven and for people who have never been through it, it's hard to infer from textbooks. And there have been periods where the market has been down for near a decade. If you put a lump sum at the 2000 peak, you wouldn't be back to even until the 2007 peak.. at which point it promptly crashed and didn't make back to even until 2013. (+/- a few years when you factor in dividends). Similar for 1973/1980/1982. Slow grind downs like the GFC are harder to experience as you watch slow losses pile up day after day for near 18 months.
- brnaftr361 3y ago
  I dunno MS took a really long time to recover it's peak. Even if you didn't buy the top it stayed flat for a very long time. Not that it happens in every instance, but at some point in managing it you have to consider opportunity cost, call a loser a loser, and pull out. 15 years to break even and that's without taking inflation into account.
  - stouset 3y ago
    Playing individual stocks is a fool’s game. Yes, the random stock you pick could turn out to be a terrible investment for any number of reasons.
bitshiftfaced 3y ago
The sharpe ratio is a common metric used to balance risk and reward. Based on the figures in this article, I'm almost positive that "lump sum" would outperform DCA's sharpe as well. A good way to respond to your example would also be to bring in a discussion of the St. Petersburg paradox and expected utility theory.
- seanhunter 3y ago
  I don't think Sharpe is the right metric here and it has the same flaw as the article. Neither the article nor the sharpe ratio would take into account the fact that in his test much of the capital would remain uninvested for the begining of the dollar cost averaging strategy so it would seem to underperform literally because far less capital would be put to work for the beginning of the test period. The use case for lump sum and dollar cost averaging (or "Systematic investment" that he mentions in the article, which sounds very much like what I have always called DCA but whatever) are different. Most people don't have a chunk of cash to invest, most people have some small amount of excess cash to invest each month or whatever. So in that world are you better off investing each month, or saving up until you have a lump sum? Almost certainly investing[1] each month. For that reason, most people in the investment world would use some variant on internal rate of return here, which you could do a risk-adjusted variant of if you wanted to. I expect if you used either of those metrics you would find that DCA pays a small amount of excess return in cases when you would luck out and invest big after a decline in the lump sum case. In return for this, DCA has far lower variance, and far less likelihood of "effective ruin"[2]. [1] Technically if your savings amount each month is very small the transaction costs will eat up your capital if you trade too often so you should save until you have chunkier amounts in that case to mitigate this. [2] Strictly if you're just investing long in cash equities (not derivs) risk of ruin is practically zero, but for a real person you can be very significantly harmed if say you bought equities at some high water mark, there is a big sell-off, the market basically goes sideways (declines in real terms after inflation) for a long period of time and you have to retire (so you have no earning power) and have to sell gradually at a loss to sustain your standard of living in retirement. This is effectively the position a lot of Japanese investors found themselves in after the big slump there.
NotYourLawyer 3y ago
Utility isn’t linear in dollars. I’d be just about as happy with 100 million as 500 million.
- Vecr 3y ago
  Even if you think it's linear, there's no reason why you need to be a dollar maximizer, or even an average dollar maximizer. You could instead maximze the 85th percentile dollar value or something like that to be more safe.
- rufus_foreman 3y ago
  How do you know? When I first started investing and only had a little money, I remember thinking that if I had twice as much, my money worries would be over. Many years later, I have 50 times as much money as then, and part of me still thinks that if I had twice as much as I have now, my money worries would be over. And the other part knows that I am just the type of person who constantly worries about money.
  - throw0101b 3y ago
    >> Utility isn’t linear in dollars. > How do you know? Empirical evidence: > Technically, the researchers found that life satisfaction rises with the log of income[1] (i.e. multiples of income), not linear changes in income. The reason why log income is more relevant here is because someone with $10,000 might be much happier than someone with $0. However, someone with $10,010,000 is probably no happier than someone with $10,000,000. In other words, $10,000 means a lot to someone with nothing, but nothing to someone with a lot. I’ve written on how this idea applies to wealth[2] in the past and I plan on expanding on it in the future. […] > In 2021, a study by Matthew Killingsworth[3] titled “Experienced well-being rises with income, even above $75,000 per year” shook the foundations of happiness research by contradicting the findings from Kahneman and Deaton’s famed 2010 paper. In particular, Killingsworth’s study found that both life satisfaction and emotional well-being continued to increase with income (i.e. the log of income), even beyond the $75,000 threshold reported by Kahneman and Deaton. * https://ofdollarsanddata.com/money-cant-buy-happiness/ https://ofdollarsanddata.com/money-cant-buy-happiness/
readthenotes1 3y ago
Your once in a lifetime trade is flawed in 2 ways: 1. the S&P 500 has never gone completely to zero. It is not the typical gamble where you lose the entirety of your bet if the random doesn't happen your way. 2. you're assuming that it is an event instead of an investment where time matters, where are you are making multiple bets and historically the random is in your favor. It can take 20 years for the S&P 500 to regain its former position if you include inflation, but for most people learning about investing, that is about a half of their expected investment time.
- throw0101b 3y ago
  > 1. the S&P 500 has never gone completely to zero. The S&P 500 specifically, no. But markets have gone to zero when (e.g.) there were Communist revolutions and private property went away. If you were invested in those then you'd lose the money (and if it was as a domestic investor you'd have other (political) problems as well).
  - readthenotes1 3y ago
    That is certainly a quibble. DCA is an artifact of retirement plans in Western countries, notably the United States. It is certainly possible for the United States to dissolve in an asteroid impact, but those tail risk type events are not worth worrying about for the type of investor that is going to be thinking about dollar cost averaging.

by 317070 3y ago

lordentropy 3y ago

If you have a long time horizon and invest in a broad-based index fund, why do you even care about short term volatility? If you need to withdraw money within the next few years, then yes volatility matters. But in that case, you might be better off not investing in stocks and go with less risky stuff.

steveBK123 3y ago
Everyone has a different definitions of short & long term, and the resulting volatility appetite. Volatility is also a lot easier to read and pontificate about than to experience in real time. What people do during draw downs is often emotion driven and for people who have never been through it, it's hard to infer from textbooks. And there have been periods where the market has been down for near a decade. If you put a lump sum at the 2000 peak, you wouldn't be back to even until the 2007 peak.. at which point it promptly crashed and didn't make back to even until 2013. (+/- a few years when you factor in dividends). Similar for 1973/1980/1982. Slow grind downs like the GFC are harder to experience as you watch slow losses pile up day after day for near 18 months.
brnaftr361 3y ago
I dunno MS took a really long time to recover it's peak. Even if you didn't buy the top it stayed flat for a very long time. Not that it happens in every instance, but at some point in managing it you have to consider opportunity cost, call a loser a loser, and pull out. 15 years to break even and that's without taking inflation into account.
- stouset 3y ago
  Playing individual stocks is a fool’s game. Yes, the random stock you pick could turn out to be a terrible investment for any number of reasons.

bitshiftfaced 3y ago

The sharpe ratio is a common metric used to balance risk and reward. Based on the figures in this article, I'm almost positive that "lump sum" would outperform DCA's sharpe as well. A good way to respond to your example would also be to bring in a discussion of the St. Petersburg paradox and expected utility theory.

seanhunter 3y ago
I don't think Sharpe is the right metric here and it has the same flaw as the article. Neither the article nor the sharpe ratio would take into account the fact that in his test much of the capital would remain uninvested for the begining of the dollar cost averaging strategy so it would seem to underperform literally because far less capital would be put to work for the beginning of the test period. The use case for lump sum and dollar cost averaging (or "Systematic investment" that he mentions in the article, which sounds very much like what I have always called DCA but whatever) are different. Most people don't have a chunk of cash to invest, most people have some small amount of excess cash to invest each month or whatever. So in that world are you better off investing each month, or saving up until you have a lump sum? Almost certainly investing[1] each month. For that reason, most people in the investment world would use some variant on internal rate of return here, which you could do a risk-adjusted variant of if you wanted to. I expect if you used either of those metrics you would find that DCA pays a small amount of excess return in cases when you would luck out and invest big after a decline in the lump sum case. In return for this, DCA has far lower variance, and far less likelihood of "effective ruin"[2]. [1] Technically if your savings amount each month is very small the transaction costs will eat up your capital if you trade too often so you should save until you have chunkier amounts in that case to mitigate this. [2] Strictly if you're just investing long in cash equities (not derivs) risk of ruin is practically zero, but for a real person you can be very significantly harmed if say you bought equities at some high water mark, there is a big sell-off, the market basically goes sideways (declines in real terms after inflation) for a long period of time and you have to retire (so you have no earning power) and have to sell gradually at a loss to sustain your standard of living in retirement. This is effectively the position a lot of Japanese investors found themselves in after the big slump there.

NotYourLawyer 3y ago

Utility isn’t linear in dollars. I’d be just about as happy with 100 million as 500 million.

Vecr 3y ago
Even if you think it's linear, there's no reason why you need to be a dollar maximizer, or even an average dollar maximizer. You could instead maximze the 85th percentile dollar value or something like that to be more safe.
rufus_foreman 3y ago
How do you know? When I first started investing and only had a little money, I remember thinking that if I had twice as much, my money worries would be over. Many years later, I have 50 times as much money as then, and part of me still thinks that if I had twice as much as I have now, my money worries would be over. And the other part knows that I am just the type of person who constantly worries about money.
- throw0101b 3y ago
  >> Utility isn’t linear in dollars. > How do you know? Empirical evidence: > Technically, the researchers found that life satisfaction rises with the log of income[1] (i.e. multiples of income), not linear changes in income. The reason why log income is more relevant here is because someone with $10,000 might be much happier than someone with $0. However, someone with $10,010,000 is probably no happier than someone with $10,000,000. In other words, $10,000 means a lot to someone with nothing, but nothing to someone with a lot. I’ve written on how this idea applies to wealth[2] in the past and I plan on expanding on it in the future. […] > In 2021, a study by Matthew Killingsworth[3] titled “Experienced well-being rises with income, even above $75,000 per year” shook the foundations of happiness research by contradicting the findings from Kahneman and Deaton’s famed 2010 paper. In particular, Killingsworth’s study found that both life satisfaction and emotional well-being continued to increase with income (i.e. the log of income), even beyond the $75,000 threshold reported by Kahneman and Deaton. * https://ofdollarsanddata.com/money-cant-buy-happiness/ https://ofdollarsanddata.com/money-cant-buy-happiness/

readthenotes1 3y ago

Your once in a lifetime trade is flawed in 2 ways: 1. the S&P 500 has never gone completely to zero. It is not the typical gamble where you lose the entirety of your bet if the random doesn't happen your way. 2. you're assuming that it is an event instead of an investment where time matters, where are you are making multiple bets and historically the random is in your favor. It can take 20 years for the S&P 500 to regain its former position if you include inflation, but for most people learning about investing, that is about a half of their expected investment time.

throw0101b 3y ago
> 1. the S&P 500 has never gone completely to zero. The S&P 500 specifically, no. But markets have gone to zero when (e.g.) there were Communist revolutions and private property went away. If you were invested in those then you'd lose the money (and if it was as a domestic investor you'd have other (political) problems as well).
- readthenotes1 3y ago
  That is certainly a quibble. DCA is an artifact of retirement plans in Western countries, notably the United States. It is certainly possible for the United States to dissolve in an asteroid impact, but those tail risk type events are not worth worrying about for the type of investor that is going to be thinking about dollar cost averaging.