Value Averaging

The book Value Averaging by Michael E. Edleson promises a simple mechanical strategy for beating the market over decades by routinely buying more stocks when they’re low and selling some stocks when they’re highest.  It was first published in 1991 and “has steadily grown to cult-classic status” according to William J. Bernstein in the 2007 edition.  Despite the impressive endorsements, the method doesn’t work.  Value Averaging’s supposed success depends on measuring returns incorrectly.

Dollar Cost Averaging (DCA)

As a warmup, the first investment strategy Edleson describes is Dollar Cost Averaging (DCA), which is the simple idea of investing a fixed dollar amount every month (or other fixed time period).  When the market is down, your money will buy more shares than when it is up, so your average purchase price over a year will be lower than the average share price over that year.

To illustrate the advantage of DCA, Edleson compares it to another strategy that he calls Constant Share (CS).  With CS, you buy a fixed number of shares each month.  As expected, DCA usually produces higher returns than the CS strategy.

It’s here that we get the first hint of a problem.  When would it ever make sense that someone would use the CS strategy?  People choose amounts to save based on what is going on in their lives.  It doesn’t make sense that the amount they choose to save would be dictated by some investment strategy.  Just because stocks are down, why would I choose to save less money?

One thought is that an investor might have a large lump sum and is trying to decide how to invest it over time.  However, in this case, investment return calculations must include the returns on the cash held back from the market.  However, Edleson calculates returns on only the money used to buy stocks; he ignores any other savings.

This criticism of an investment strategy dictating the amount investors choose to save from their pay isn’t very serious yet.  For a few years investors really could use the CS strategy and eat out once or twice more in a month when the strategy calls for saving less money because the market is down.

The CS strategy has another problem.  The market goes up faster than salaries do.  Over the decades it would become infeasible to keep buying the same (split-adjusted) number of shares each month.  However, this isn’t a serious concern because the CS strategy only exists to illustrate the way DCA lowers average purchase price.  It’s not offered as a serious contender for how to invest.

A Simple Version of Value Averaging (VA)

To introduce Value Averaging (VA), Edleson describes a simple version.  Suppose you want to have $2400 saved after two years of investing.  To achieve this goal, you set interim targets over the 24 months of $100, $200, …, $2400.  You then invest whatever amount is necessary each month to reach the next interim target.  So, you invest $100 the first month.  In Edleson’s example of a precious metals fund in 1986 and 1987, the first month’s return is a loss of $5.60.  So, you have to invest $105.60 the next month to reach the interim target of $200.  This continues until you have $2400 after 2 years.

You might wonder what happens if the fund earns more than $100 one month.  The answer is that you sell some of the fund to get down to your interim target.  Over the course of the two years in this example, the amounts you had to invest ranged from selling $483 worth of the fund one month all the way to having to save $703 in another month.  These swings are partly due to this being a volatile precious metals fund.  However, when investing over more than just 2 years, such swings will grow larger as your savings grow.

These amounts may not sound like much in today’s dollars, but imagine that your target today is to save $1000 per month.  Then in the book’s example scenario, VA asked you to take back $4830 one month and come up with $7030 another month.  It’s clear that you’re not going to spend $4830 on a couple of dinners, and you likely couldn’t easily come up with $7030 one month out of your pay.  To handle these large amounts, you must have a separate savings account where you’d hold cash that the VA strategy doesn’t want in the market.  Sometimes you’d add to this account, and sometimes you’d dip into to get cash to invest.  If this account runs dry, you might even borrow to satisfy VA’s demands.

Edleson suggests that you might put some money aside, “perhaps in a money market fund,” to deal with the big swings in how much money VA calls on you to save each month.  However, this side pool of savings is an integral part of VA.  When you have money on the side or you borrow, the interest on this money should be part of the VA return calculation.  However, Edleson ignores them.  He does an Internal Rate of Return (IRR) calculation on just the amounts that go into and out of the market.

Edleson calculates the IRR of VA in this example to be 20.1% (per year).  He appears to have taken the monthly IRR and multiplied it by 12.  I get the annual IRR to be 22.1% when it’s properly compounded.  However, returns change if we include the side savings in the money market fund and amounts borrowed.  Let’s assume that you save $100 per month regardless of VA’s demands.  You put any excess cash in the money market fund, and you borrow if necessary.  A quick search on prevailing rates around 1986 gave 7% interest in the money market fund and 10% interest on borrowed funds.  In this scenario, the annual IRR drops from 22.1% to 17.9%.  If you prefer not to borrow and save up $100 for two months before the start of 1986, the annual IRR drops to 16.2%.  Properly taking into account side savings and borrowing makes a big difference.

The VA returns are still better than the 4% you’d have received using DCA in this example.  However, when Edleson continued this investment scenario for another 25 months, the DCA return for the roughly 4 years rose to 6.8% and the VA return dropped to 13.8%.  After properly accounting for side savings and borrowing, it’s not clear whether VA is actually any better than DCA, even for this example.  Costs from the extra trading that VA requires in addition to income taxes if you’re investing in a taxable account further muddy the waters.

More Realistic DCA

As a further warmup below describing the full VA strategy, Edleson describes a more realistic version of DCA.  Over a short period of time, fixed monthly contributions to savings makes sense.  But over decades we expect inflation to allow us to increase contributions to savings.  So, unlike simple DCA, we assume that monthly contributions to savings grow over time.  Edleson gives formulas for calculating your portfolio level each month given your initial contributions, the contributions growth rate, expected market returns, and how long you invest.

Of course, markets won’t behave perfectly, and your portfolio won’t grow exactly according to plan.  To use this DCA plan, you’d have to periodically adjust your savings amount based on what the markets do.

Full VA

With VA, you use the annual portfolio level each month from DCA as a “value path.”  The idea with VA is that you adjust your contributions to savings each month to stay on this value path.  If markets disappoint, you have to increase your contributions.  If markets outperform your expectations, you contribute less or possibly sell some of your investments.

As in the simpler version of VA, “Always maintain a side fund” for holding excess contributions that the strategy dictates shouldn’t be invested yet, saving them for a future time when the strategy calls for large contributions.

Edleson performs a number of experiments using simulated market returns and other experiments with actual historical market returns.  Across each type of scenario, the average advantage of VA over DCA is always less than 1.4%.  However, this is always the result of measuring VA returns improperly by ignoring the side fund.  The drag on returns from holding cash and possibly borrowing makes it doubtful that VA actually beats DCA.

Conclusion

The most serious criticism of value averaging is that because returns aren’t measured correctly, there is no evidence that the method works better than simpler investment strategies.  This flaw alone is likely fatal to all variants of VA proposed in this book.

Here are other articles I’ve written about value averaging:

Value Averaging Doesn’t Work
Value Averaging Nonsense
Value Averaging Experiments

2020-11-18 A Technical Addition:

The VA recommended value path is based on DCA with a starting contribution of C and a monthly growth rate g (C, C(1+g), C(1+g)^2, ...).  Assuming monthly return r, the book gives the value path formula for the future value after t months:

V(t) = C((1+r)^t - (1+g)^t)/(r-g).

Actually, this formula only works when r is not equal to g.

When r=g, V(t) = Ct(1+g)^(t-1).

The formula for V(t) involves 5 different quantities: C, g, r, t, and V(t).  The book devotes many pages to methods of calculating one of these 5 values when given the other 4.  It also gives elaborate spreadsheets for this task.  There are much simpler approaches using common spreadsheet functions.

If either V(t) or C is the only unknown, the calculation is straightforward.  To find g or r:

g = (1+RATE(t, -C, 0, V(t)/((1+r)^(t-1))))*(1+r)-1.
r = (1+RATE(t, -C, 0, V(t)/((1+g)^(t-1))))*(1+g)-1.

Finding t given the other 4 values is trickier, but can be done using Newton's method.  Start by calculating an estimate for t (call it t_0) that ignores g:

t_0 = NPER(r, -C, 0, V(t)).

Then calculate estimates for V(t) and its derivative based on the estimate t_0:

V_0 = C*IF(ABS(r-g)>0.000001, ((1+r)^t_0-(1+g)^t_0)/(r-g),
           t_0*(1+(r+g)/2)^(t_0 - 1)).
D_0 = C*IF(ABS(r-g)>0.000001, (LN(1+r)*(1+r)^t_0 - LN(1+g)*(1+g)^t_0)/(r-g),
           (1+t_0*LN(1+(r+g)/2))*(1+(r+g)/2)^(t_0 - 1)).

Then complete the Newton iteration to get t_1, a better estimate of t:

t_1 = t_0 - (V_0 - V(t))/D_0.

The repeat these 3 formulas using t_1 to get a new estimate t_2.  Repeat to get t_3, t_4, and t_5.  I have found that just 5 iterations are enough so that t_5 is an accurate estimate of t to several decimal places.