"Principal protection" is a term one hears a lot these days as investors look for safe places to stash their money during the current downturn. Investments like money market funds and individual Treasury bonds offer principal protection. It's easy to see why the idea of not being at risk of losing principal is very appealing. Unfortunately, investors get a little carried away with this idea.
To begin with, people put too much emphasis on not losing money. 0% is one point along a spectrum of possible returns. It's a little bit worse than +1% and a little bit better than -1%. People who make principle protection the be-all and end-all of their investment strategy are effectively saying that there is a very sharp "cliff" between 0% and -1% and that by all means they do not want to fall off that cliff. This imaginary cliff can distort one's comparison of different investment options.
Perhaps the more critical point, though, is that investments like money market funds and individual bonds do not offer principal protection in the only currency that really matters; i.e., purchasing power. Due to inflation, the dollars you get out when a bond matures may have significantly less purchasing power than the dollars you put in when you purchased that bond. So you really do not get principal protection in any sense that really matters.
This mistaken attraction to the siren song of principal protection might be considered harmless, but I think it has been used, or abused, by financial advisors to steer investors towards one particular investment choice that often does not make sense for them; namely, towards individual bonds rather than bond mutual funds. One of the main selling points touted for individual bonds is, in fact, principal protection, which a bond mutual fund cannot offer. However, in my opinion, a bond mutual fund is generally a better choice for the individual investor. A bond mutual fund will offer better diversification, better liquidity and lower costs. The last advantage may not be understood by many investors, because the costs in buying and selling individual bonds are often hidden to the investor. They may be embedded in bid/ask spreads, for example.
Sunday, January 4, 2009
Monday, October 20, 2008
Constantinides's Argument
Another day, another article about dollar-cost averaging. I just finished skimming through "A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy" by George Constantinides. The core argument there is quite devastating, I feel, and can be explained at an intuitive level without any of the mathematical apparatus from the paper.
To set the stage first note that although we've talked about dollar-cost averaging as a strategy for shifting money from a safe investment (cash) to a risky investment (stocks), an adherent of dollar-cost averaging should equally well recommend the same approach when moving from stocks to cash (or, in general, from any asset class to any other asset class). The core argument still applies: you want to enhance your chances of getting a "fair" price for the stock and not run the risk of a bad price by happening to be very unlucky in your choice of the day for the lump sum transition. Whether you happen to be buying or selling the stock, the logic is the same.
Second, note that we've implicitly been assuming all along that there are no transactions costs of any sort. We can instantly and without cost shift any part of our portfolio from one asset to another without paying commissions, capital gains tax, or anything like that. Of course, this is an idealization, but it seems like a harmless one. Certainly the proponents of dollar-cost averaging don't argue that the reason the approach works is because of transaction costs. (If anything, transactions costs hurt the case for dollar-cost averaging since you have more transactions.)
Now consider two investors John and Mary. John has inherited $1,000,000 in cash while Mary has inherited $1,000,000 in stock. Let's call that point in time t0. They have identical preferences as far as risk and return and each feel their optimal long-term allocation is 50% stocks and 50% cash. If we subscribe to dollar-cost averaging, at t0 John should move a little money into stocks and Mary should move a little money into cash. But clearly they will still have different portfolios: John will still be mostly in cash, and Mary will still be mostly in stocks.
Now here's where the trap closes on the hapless DCA proponent. Observe that John and Mary are really in equivalent positions at t0. By our assumption above of no transaction costs, Mary can move all her money from stocks to cash at t0 without any cost (and vice versa for John). If Mary can transition freely and instantaneously to John's portfolio at t0, and John can transition freely and instantaneously to Mary's portfolio at t0, how can they possibly have different optimal investment strategies to pursue at t0?
To put it another way, suppose we can quantify John's utility at t0 (after he readjusts his portfolio as per DCA) as Uj,0 and Mary's utility at t0 as Um,0. This utility will be a function of the expected return and volatility of their portfolio going forward from t0. If Uj,0 > Um,0 then you have to wonder why Mary doesn't just shift all her money to John's portfolio at t0 which would give her utility Uj,0. Likewise if Um,0 > Uj,0. The only way we don't get a contradiction is if Uj,0 = Um,0 but in general that is not going to be the case - a 95% allocation to stocks and a 95% allocation to cash will not offer identical utility.
To set the stage first note that although we've talked about dollar-cost averaging as a strategy for shifting money from a safe investment (cash) to a risky investment (stocks), an adherent of dollar-cost averaging should equally well recommend the same approach when moving from stocks to cash (or, in general, from any asset class to any other asset class). The core argument still applies: you want to enhance your chances of getting a "fair" price for the stock and not run the risk of a bad price by happening to be very unlucky in your choice of the day for the lump sum transition. Whether you happen to be buying or selling the stock, the logic is the same.
Second, note that we've implicitly been assuming all along that there are no transactions costs of any sort. We can instantly and without cost shift any part of our portfolio from one asset to another without paying commissions, capital gains tax, or anything like that. Of course, this is an idealization, but it seems like a harmless one. Certainly the proponents of dollar-cost averaging don't argue that the reason the approach works is because of transaction costs. (If anything, transactions costs hurt the case for dollar-cost averaging since you have more transactions.)
Now consider two investors John and Mary. John has inherited $1,000,000 in cash while Mary has inherited $1,000,000 in stock. Let's call that point in time t0. They have identical preferences as far as risk and return and each feel their optimal long-term allocation is 50% stocks and 50% cash. If we subscribe to dollar-cost averaging, at t0 John should move a little money into stocks and Mary should move a little money into cash. But clearly they will still have different portfolios: John will still be mostly in cash, and Mary will still be mostly in stocks.
Now here's where the trap closes on the hapless DCA proponent. Observe that John and Mary are really in equivalent positions at t0. By our assumption above of no transaction costs, Mary can move all her money from stocks to cash at t0 without any cost (and vice versa for John). If Mary can transition freely and instantaneously to John's portfolio at t0, and John can transition freely and instantaneously to Mary's portfolio at t0, how can they possibly have different optimal investment strategies to pursue at t0?
To put it another way, suppose we can quantify John's utility at t0 (after he readjusts his portfolio as per DCA) as Uj,0 and Mary's utility at t0 as Um,0. This utility will be a function of the expected return and volatility of their portfolio going forward from t0. If Uj,0 > Um,0 then you have to wonder why Mary doesn't just shift all her money to John's portfolio at t0 which would give her utility Uj,0. Likewise if Um,0 > Uj,0. The only way we don't get a contradiction is if Uj,0 = Um,0 but in general that is not going to be the case - a 95% allocation to stocks and a 95% allocation to cash will not offer identical utility.
Saturday, October 18, 2008
A Better Demonstration
One of these days I'll write about a topic other than dollar-cost averaging. Today is not that day.
I think I've come up with a better way to demonstrate the futility of dollar-cost averaging that sidesteps some of the complexity we got mired in back in my earlier posts. It relies on computer simulation to compare a hypothetical dollar-cost-averaging approach to a "lump sum investment" approach.
Let's say we have a portfolio that is at this moment 100% cash and 0% stocks. You want to use dollar-cost averaging to transition your portfolio gradually to 100% stocks over some initial period of time. After that you are going to hold the all-stock portfolio for some period of time. You can pick the initial duration (the length of the "ramp up" period) and the "steady state" duration to be whatever you like.
My claim is that whatever values you select, I can construct a superior portfolio that takes a "lump sum investment" approach. This portfolio will start with X% of its funds allocated to stock and maintain exactly that percentage for the full duration - i.e., we have a lump sum investment at the very beginning of the experiment. This portfolio will be superior to the DCA portfolio because it will have an identical expected return, but the volatility - measured as the standard deviation of the observed returns - will be lower.
As you might guess, X will be chosen so that the average allocation to stocks - across the entire time period - is the same for the lump sum investment approach as for the DCA approach.
My main assumption is that the return of stocks over a single unit of time is drawn from a normal distribution and is independent of the return of stocks over any other unit of time.
I ran the simulation with these parameters, but, again, the assertion is that I could choose essentially any set of values:
Dollar-cost averaging:
Means: 2833.938-2836.723
Stddevs: 879.314-883.154
Lump-sum investment:
Means: 2834.745-2837.861
Stddevs: 863.836-866.589
As you can see, the means fall very close to each other, but the standard deviations of the lump-sum approach are lower. Perhaps not hugely lower, but clearly there is a difference that is not random noise.
I think I've come up with a better way to demonstrate the futility of dollar-cost averaging that sidesteps some of the complexity we got mired in back in my earlier posts. It relies on computer simulation to compare a hypothetical dollar-cost-averaging approach to a "lump sum investment" approach.
Let's say we have a portfolio that is at this moment 100% cash and 0% stocks. You want to use dollar-cost averaging to transition your portfolio gradually to 100% stocks over some initial period of time. After that you are going to hold the all-stock portfolio for some period of time. You can pick the initial duration (the length of the "ramp up" period) and the "steady state" duration to be whatever you like.
My claim is that whatever values you select, I can construct a superior portfolio that takes a "lump sum investment" approach. This portfolio will start with X% of its funds allocated to stock and maintain exactly that percentage for the full duration - i.e., we have a lump sum investment at the very beginning of the experiment. This portfolio will be superior to the DCA portfolio because it will have an identical expected return, but the volatility - measured as the standard deviation of the observed returns - will be lower.
As you might guess, X will be chosen so that the average allocation to stocks - across the entire time period - is the same for the lump sum investment approach as for the DCA approach.
My main assumption is that the return of stocks over a single unit of time is drawn from a normal distribution and is independent of the return of stocks over any other unit of time.
I ran the simulation with these parameters, but, again, the assertion is that I could choose essentially any set of values:
- Expected stock return: 0.01 (meaning expected appreciation of stocks over one unit of time is 1%)
- Standard deviation of stock returns: 0.03
- Return on cash: 0 (with no variability)
- Length of "ramp up" period: 10 time units
- Length of "steady state" period: 100 time units
- Starting value of portfolio: $1000
Dollar-cost averaging:
Means: 2833.938-2836.723
Stddevs: 879.314-883.154
Lump-sum investment:
Means: 2834.745-2837.861
Stddevs: 863.836-866.589
As you can see, the means fall very close to each other, but the standard deviations of the lump-sum approach are lower. Perhaps not hugely lower, but clearly there is a difference that is not random noise.
Monday, October 13, 2008
Response to Comments
I thought I'd respond to some of the comments in the main blog rather than limit all of the interesting discussion to the comments section.
Remco writes:
Second, I would assert that the only rational way to measure risk or return to compute them with respect to your whole portfolio. It's true that dollar-cost averaging will ensure that you don't buy the stock at a local minimum or maximum. Over a sufficiently short time period, it will also reduce the variance in your return on that stock over that period. But so what? What you should really care about is your overall net worth, and the variance on that. Imagine that you keep your money in your left pocket and your right pocket. It would be irrational to make decisions based solely on the returns and volatility of your "right pocket" money. My earlier posts lay out the argument why dollar-cost averaging has no value when looking at your portfolio overall.
Dollar-cost averaging is clearly marketed to people as something that would be beneficial to them. It's possible that those marketing it only directly point out that they are going to get a "fairer" price for the stock. But it's implicit that this matters, that this is beneficial to their overall financial situation.
Remco writes:
I think its purpose is exactly what its name implies, which is to purchase (or sell) stock at a short-term average price.... Dollar cost averaging tries to makes sure you get a "fair" price, i.e., that you don't buy stock at a local maximum or sell it at a local minimum. What you get is a reduction in risk (clearly), at the expense of reduced returns (because stock goes up on average and hence you end up paying more / getting less, on average).Two responses. First, I agree and have already pointed out that dollar-cost averaging does reduce risk as compared to a lump-sum investment. But the reason it reduces risk is because you are holding a lot of cash during the transition period, not because that gradual transitioning process has some variance-reducing power over and above that. My assertion is that if it is suboptimal (because too risky) for you to hold the entire amount in stocks, then the rational thing to do is to simply reduce the amount you move into stocks. In general, to control variance, reduce the amount you assign to the riskiest asset class; but always make a lump-sum shift into your target allocation. If you want to argue for dollar-cost averaging, you should argue not just that it reduces variance, but that it reduces variance in a way superior to the alternatives (e.g., simply continuing to hold some cash).
Second, I would assert that the only rational way to measure risk or return to compute them with respect to your whole portfolio. It's true that dollar-cost averaging will ensure that you don't buy the stock at a local minimum or maximum. Over a sufficiently short time period, it will also reduce the variance in your return on that stock over that period. But so what? What you should really care about is your overall net worth, and the variance on that. Imagine that you keep your money in your left pocket and your right pocket. It would be irrational to make decisions based solely on the returns and volatility of your "right pocket" money. My earlier posts lay out the argument why dollar-cost averaging has no value when looking at your portfolio overall.
Dollar-cost averaging is clearly marketed to people as something that would be beneficial to them. It's possible that those marketing it only directly point out that they are going to get a "fairer" price for the stock. But it's implicit that this matters, that this is beneficial to their overall financial situation.
Friday, October 10, 2008
Dollar-Cost Averaging Revisited
I want to back up and try to restate my argument against dollar-cost averaging, and maybe make it a tad more explicit in the process. My original post didn't spell out a lot of the assumptions I was making.
The central point of my argument against dollar-cost averaging is that the (expected) risk-adjusted return of a portfolio is time-invariant. (Although I don't actually quite believe that - see below.) Implicitly, I am using "risk-adjusted return" as an overall goodness measure of a portfolio. In other words, your only objective as an investor is to select a portfolio that maximizes the risk-adjusted return. Once we accept that your risk-adjusted return is time-invariant, then it follows immediately that dollar-cost averaging is irrational, because dollar-cost averaging is a specific way of varying your portfolio over time which is alleged to be beneficial.
So what exactly is "risk-adjusted return"? Well, different people might define it in different ways. Obviously the expected return of the portfolio should play a role. (For example, a portfolio with an expected annual return of 10% would be preferable, all other things being equal, to a portfolio with an expected annual return of 5%.) Additionally, most people would agree that some measure of risk or volatility should contribute. Given a choice between a portfolio that always yields exactly 10% annually, and one that has an expected return of 10% but may be much higher or lower, it is natural to assume that a rational investor would choose the former. How do you measure risk or volatility? Typically people use the standard deviation of the return, but you could probably use a different measure without affecting the present argument. How do we combine the expected return of the portfolio with the risk measure (e.g., standard deviation)? Again, different people will do it differently and it ultimately may not matter for our purposes. But, for concreteness, we could use the Sharpe ratio.
Why then should we believe that risk-adjusted return is time-invariant? Well, there are good theoretical reasons to believe that expected returns are time-invariant, stemming from the idea that markets are reasonably efficient. Suppose expected returns were not time-invariant; in other words, we have reason to believe that the returns of some asset class will be higher or lower at some point in the future than the expected return over the long run. Well, we would presumably take advantage of that fact. For example, if we thought stocks were about to perform poorly in the near future we would sell them today; if we thought they were about to shoot up, we would buy them. Furthermore, the market is full of smart people looking for any edge; it would be unrealistic to expect ourselves to be the only people with this information. Enough people trying to exploit this "mispricing" will force prices down to their "true" value. So, contrary to assumption, in an efficient market we do not expect there to be mispricings of this sort. Or, at least, we do not expect them to be large and we do not expect them to persist long enough for an amateur investor to take advantage of.
Unfortunately, I don't think there are similar arguments that expected volatility must be time-invariant. As I write this in October of 2008, we are in the middle of one of the biggest market crashes of the century. I do not know whether the market will move up or down over the next few weeks, but I do have good reason to believe that volatility will be unusually high. Knowledge about future volatility cannot be arbitraged away (it seems to me), so there is no reason for it not to exist.
Still, this doesn't really constitute an argument for dollar-cost averaging. I can see some grounds for making some adjustments (probably minor) to your portfolio over time depending on your expectations of future volatility. But, as I mentioned in my original post, the kind of gradual portfolio shift entailed by dollar-cost averaging, would only be sensible in the highly unusual circumstance where you have information that volatility will be high in the near future, but will gradually decrease over time.
The central point of my argument against dollar-cost averaging is that the (expected) risk-adjusted return of a portfolio is time-invariant. (Although I don't actually quite believe that - see below.) Implicitly, I am using "risk-adjusted return" as an overall goodness measure of a portfolio. In other words, your only objective as an investor is to select a portfolio that maximizes the risk-adjusted return. Once we accept that your risk-adjusted return is time-invariant, then it follows immediately that dollar-cost averaging is irrational, because dollar-cost averaging is a specific way of varying your portfolio over time which is alleged to be beneficial.
So what exactly is "risk-adjusted return"? Well, different people might define it in different ways. Obviously the expected return of the portfolio should play a role. (For example, a portfolio with an expected annual return of 10% would be preferable, all other things being equal, to a portfolio with an expected annual return of 5%.) Additionally, most people would agree that some measure of risk or volatility should contribute. Given a choice between a portfolio that always yields exactly 10% annually, and one that has an expected return of 10% but may be much higher or lower, it is natural to assume that a rational investor would choose the former. How do you measure risk or volatility? Typically people use the standard deviation of the return, but you could probably use a different measure without affecting the present argument. How do we combine the expected return of the portfolio with the risk measure (e.g., standard deviation)? Again, different people will do it differently and it ultimately may not matter for our purposes. But, for concreteness, we could use the Sharpe ratio.
Why then should we believe that risk-adjusted return is time-invariant? Well, there are good theoretical reasons to believe that expected returns are time-invariant, stemming from the idea that markets are reasonably efficient. Suppose expected returns were not time-invariant; in other words, we have reason to believe that the returns of some asset class will be higher or lower at some point in the future than the expected return over the long run. Well, we would presumably take advantage of that fact. For example, if we thought stocks were about to perform poorly in the near future we would sell them today; if we thought they were about to shoot up, we would buy them. Furthermore, the market is full of smart people looking for any edge; it would be unrealistic to expect ourselves to be the only people with this information. Enough people trying to exploit this "mispricing" will force prices down to their "true" value. So, contrary to assumption, in an efficient market we do not expect there to be mispricings of this sort. Or, at least, we do not expect them to be large and we do not expect them to persist long enough for an amateur investor to take advantage of.
Unfortunately, I don't think there are similar arguments that expected volatility must be time-invariant. As I write this in October of 2008, we are in the middle of one of the biggest market crashes of the century. I do not know whether the market will move up or down over the next few weeks, but I do have good reason to believe that volatility will be unusually high. Knowledge about future volatility cannot be arbitraged away (it seems to me), so there is no reason for it not to exist.
Still, this doesn't really constitute an argument for dollar-cost averaging. I can see some grounds for making some adjustments (probably minor) to your portfolio over time depending on your expectations of future volatility. But, as I mentioned in my original post, the kind of gradual portfolio shift entailed by dollar-cost averaging, would only be sensible in the highly unusual circumstance where you have information that volatility will be high in the near future, but will gradually decrease over time.
Saturday, September 13, 2008
The Psychology of Dollar-Cost Averaging, Part Two
Kahneman and Tversky are also well-known for exploring the phenomenon of "loss aversion". Wikipedia sums up the phenomenon, saying "Loss aversion implies that one who loses $100 will lose more satisfaction than another person will gain satisfaction from a $100 windfall." Kahneman and Tversky came up with an ingenious set of experiments where they frame the same problem in different ways - in one case describing something as a potential loss and in another describing it as a potential gain - and found that people made different choices in the different situations even though there was no real economic difference between the two. When something was framed as a potential loss, people were more risk averse than when it was framed as a potential gain.
Part of the appeal of dollar-cost averaging is the fear that if we suddenly shift all our money into stocks, the market could tumble tomorrow and we would lose a lot of money. However, it could equally well be pointed out that the market could skyrocket tomorrow, and we could end up with a lot more money than we would have with dollar-cost averaging. Since our current portfolio with the money in cash is regarded as the baseline, the first scenario is regarded as a loss and the second scenario is regarded as a gain. So loss aversion could be the explanation of why we don't treat the two possibilities symmetrically and why the potential scenario of the market dropping tomorrow is unduly influential.
Part of the appeal of dollar-cost averaging is the fear that if we suddenly shift all our money into stocks, the market could tumble tomorrow and we would lose a lot of money. However, it could equally well be pointed out that the market could skyrocket tomorrow, and we could end up with a lot more money than we would have with dollar-cost averaging. Since our current portfolio with the money in cash is regarded as the baseline, the first scenario is regarded as a loss and the second scenario is regarded as a gain. So loss aversion could be the explanation of why we don't treat the two possibilities symmetrically and why the potential scenario of the market dropping tomorrow is unduly influential.
Saturday, September 6, 2008
The Psychology of Dollar-Cost Averaging, Part One
Continuing on the topic of dollar-cost averaging, I have some theories about the psychological factors that make dollar-cost averaging appealing. It may be helpful to consider an analogy. Suppose we are contemplating walking up to the edge of a very high and steep cliff in windy weather. Rather than just striding directly to the edge, you would probably approach slowly, testing your footing at each step. This slow approach to the precipice is the analog to dollar-cost averaging. We gradually transition from a safer position (standing back from the edge, or holding a sum of money in cash) to a riskier position (standing right on the edge, or putting all of that sum of money in stocks). This gradual transitioning makes sense in the context of approaching the edge of a cliff. However, as I will show, this situation is not analogous to the financial case in the crucial respects.
In the case of approaching the edge of a cliff, the risks are somewhat unknown. We may not know how stable the footing is, how strong the winds are, or how disoriented we will become by the prospect of the sheer drop. In the face of such uncertainty, it makes sense to gradually ramp up the risk, turning back if the riskiness exceeds our tolerance. At each step, we reassess - we test our footing, we see if we can maintain an upright posture and a sense of balance - and we gain new information about how safe we are. It is this uncertainty about the true riskiness - and the ability to reassess it at each step - that makes the gradual transitioning process rational.
The financial situation is quite different. To begin with, you cannot accurately assess the riskiness of holding stocks by observing the market for a month. Over a one-month period, the market may perform much better than expectation or much worse than expectation. It may be much more volatile than normal, or much less. One month, or even a year, is not really enough to learn anything. So the element of learning something as you "approach the precipice" gradually is not present here.
In general, the way to gauge the riskiness of stocks (or any other asset class) is by looking at their behavior over a long period of time. For example, we might look at their performance and volatility over the past 100 years. Once we have done so, we have essentially all the information we are going to have regarding their riskiness. Another one month of observation is not going to add much value. So, unlike the cliff example, the riskiness is known in advance (to the extent that it is knowable) and there is no information to be gained by the gradual transitioning.
I should acknowledge that dollar-cost averaging may be rational for some based on psychological considerations. For example, suppose you don't know how well you will sleep at night, after you invest your money in the market, given the substantial volatility of stocks. In this case, you cannot quantify your gains or losses in purely dollar terms - you are also concerned about the effects on your mental health, which may not be knowable until you experience the daily swings "first hand". In such a case, it may be rational to enter the market gradually, reassessing your mental state as you go. Even so, it still needs to be said that this process may give you a false sense of confidence in that the market may not experience a major correction during the period in which you are performing the transition.
But, more generally, for the investor who will not be anguished by losses - or who can assess and account for such psychological considerations in advance - dollar-cost averaging offers no real advantages.
This kind of irrationality is the sort of thing people in Behavioral Economics study. Some readers may be familiar with the work of Kahneman and Tversky which, as I understand it, was the inspiration and foundation for this field. It would be interesting to know if anyone working within Behavioral Economics has studied why dollar-cost averaging appeals to people.
In the case of approaching the edge of a cliff, the risks are somewhat unknown. We may not know how stable the footing is, how strong the winds are, or how disoriented we will become by the prospect of the sheer drop. In the face of such uncertainty, it makes sense to gradually ramp up the risk, turning back if the riskiness exceeds our tolerance. At each step, we reassess - we test our footing, we see if we can maintain an upright posture and a sense of balance - and we gain new information about how safe we are. It is this uncertainty about the true riskiness - and the ability to reassess it at each step - that makes the gradual transitioning process rational.
The financial situation is quite different. To begin with, you cannot accurately assess the riskiness of holding stocks by observing the market for a month. Over a one-month period, the market may perform much better than expectation or much worse than expectation. It may be much more volatile than normal, or much less. One month, or even a year, is not really enough to learn anything. So the element of learning something as you "approach the precipice" gradually is not present here.
In general, the way to gauge the riskiness of stocks (or any other asset class) is by looking at their behavior over a long period of time. For example, we might look at their performance and volatility over the past 100 years. Once we have done so, we have essentially all the information we are going to have regarding their riskiness. Another one month of observation is not going to add much value. So, unlike the cliff example, the riskiness is known in advance (to the extent that it is knowable) and there is no information to be gained by the gradual transitioning.
I should acknowledge that dollar-cost averaging may be rational for some based on psychological considerations. For example, suppose you don't know how well you will sleep at night, after you invest your money in the market, given the substantial volatility of stocks. In this case, you cannot quantify your gains or losses in purely dollar terms - you are also concerned about the effects on your mental health, which may not be knowable until you experience the daily swings "first hand". In such a case, it may be rational to enter the market gradually, reassessing your mental state as you go. Even so, it still needs to be said that this process may give you a false sense of confidence in that the market may not experience a major correction during the period in which you are performing the transition.
But, more generally, for the investor who will not be anguished by losses - or who can assess and account for such psychological considerations in advance - dollar-cost averaging offers no real advantages.
This kind of irrationality is the sort of thing people in Behavioral Economics study. Some readers may be familiar with the work of Kahneman and Tversky which, as I understand it, was the inspiration and foundation for this field. It would be interesting to know if anyone working within Behavioral Economics has studied why dollar-cost averaging appeals to people.
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