Dollar Cost Averaging DCA: invest gradually in equal dollar amounts, - - PDF document

Why Dollar Cost Averaging Doesn’t Work

• And Why Investors Use It Anyway

Simon Hayley Cass Business School

Dollar Cost Averaging

 DCA: invest gradually in equal dollar amounts, rather

than investing the desired total in one lump sum.

 Proponents argue:

 Profits increased, since DCA’s average cost always

below average price.

 Lower risk  Useful discipline

Price Shares Cost 1 $3 20 $60 2 $1 60 $60 3 $2 30 $60 110 $180 (a) DCA DCA average cost $1.64 Average price $2.00

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DCA Is Mean-Variance Inefficient

 Strategies which pre-commit investors are dominated by

strategies which allow investors to react to incoming news (Constantinides,1979).

 Making many small purchases does not diversify. DCA is

most sensitive to returns in the later part of the period. Better diversification is achieved by investing in one initial lump sum and thus being fully exposed in each period (Rozeff, 1994).

 Empirical studies: investing in one lump sum has generally

given better mean-variance performance than DCA, eg. Knight and Mandell (1992/93), Williams and Bacon (1993), Rozeff (1994), Thorley (1994).

So why is DCA still so popular?

 Previous answers:  Non-variance risk preferences  Forecastable markets  Non-profit motives (behavioural finance)  But DCA is recommended to investors regardless of

their expectations or preferences or the market involved.

DCA’s Low Average Purchase Cost

 Comparing the average cost under DCA with the

average price sounds entirely sensible.

 It implicitly compares DCA with a strategy of investing

the same total amount by buying a fixed number of shares each period.

Price Shares Cost Shares Cost Shares Cost 1 $3 20 $60 20 $60 30 $90 2 $1 60 $60 20 $20 30 $30 3 $2 30 $60 20 $40 30 $60 110 $180 60 $120 90 $180 (b) ESA1 (c) ESA2 (a) DCA Price Shares Cost Shares Cost Shares Cost 1 $3 20 $60 20 $60 15 $45 2 $4 15 $60 20 $80 15 $60 3 $5 12 $60 20 $100 15 $75 47 $180 60 $240 45 $180 (b) ESA1 (c) ESA2 (a) DCA

 Comparing DCA’s average cost with the average price

compares DCA with a strategy which:

 Buys equal numbers of shares each period  Invests the same total amount  But this is a strategy which:  Requires knowledge of future prices  Uses this knowledge to reduce profits

(invest more if prices will fall/ less is they will rise)

 Unsurprisingly, DCA looks good when compared with

such as strategy!

Could inefficient markets justify use of DCA?

 This is not how DCA is ‘sold’ to investors.  DCA would be a very unattractive strategy for investors

who believe that they can forecast market returns.

 Historical return data show DCA underperforming.

DCA is inefficient regardless of investor risk preferences

 We can demonstrate that DCA is a sub-optimal strategy

by showing that an alternative strategy can generate the same outturns at a lower initial cost (Dybvig, 1988).

 This shows that DCA is an inefficient strategy regardless

• f investor risk preferences.

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Terminal Wealth Rank State Price Density(x81) 480 1 UUUU 16 240 112 120 6 UUUD 32 16 144 4 UUDU 32 72 48 36 12 UUDD 64 32 192 3 UDUU 32 96 40 48 11 UDUD 64 16 72 8 UDDU 64 36 Equities: 16 18 15 UDDD 128 Cash: 48 288 2 DUUU 32 144 64 72 8 DUUD 64 16 96 7 DUDU 64 48 24 24 14 DUDD 128 32 144 4 DDUU 64 72 28 36 12 DDUD 128 16 60 10 DDDU 128 30 15 16 DDDD 256

DCA Strategy

Total Terminal Wealth Terminal Wealth Rank State Price Density (x81) 480.0 1 UUUU 16 224.0 112.0 32.0 144.0 4 UUUD 32 32.0 144.0 4 UUDU 32 56.0 58.7 32.0 60.0 10 UUDD 64 26.7 192.0 3 UDUU 32 96.0 40.0 0.0 48.0 11 UDUD 64 16.0 72.0 8 UDDU 64 36.0 Equities: 23.1 0.0 18.0 15 UDDD 128 Cash: 39.1 288.0 2 DUUU 32 144.0 64.0 0.0 72.0 8 DUUD 64 16.0 96.0 7 DUDU 64 48.0 29.3 0.0 24.0 14 DUDD 128 21.3 120.0 6 DDUU 64 56.0 28.0 8.0 36.0 12 DDUD 128 8.0 36.0 12 DDDU 128 14.0 8.0 15.0 16 DDDD 256

…A Cheaper Alternative

Same Outurns Lower Cost

Possible Behavioural Finance Effects

 DCA requires regular investment. This prevents investor

myopia, which might otherwise lead to insufficient saving. It also prevents investors from trying to time the market.

 Fewer feelings of regret about ill-timed investments.  Reduced average cost also flatters investors.

It is up to investors/advisors to judge whether these psychological benefits outweigh the inefficiency of DCA. Clarity about why DCA does not increase returns should help make the right decision.

Conclusion - Why DCA Does Not work

 Comparing DCA’s average cost with the average price

sounds reasonable, but in fact it compares DCA with a strategy which uses perfect foresight to invest badly.

 Investing gradually is inefficient.  Investors more exposed to later returns than to

earlier returns.

 Investing immediately gives better diversification.

Conclusion - Why Investors Still Use DCA

 DCA long known to be mean-variance inefficient. Previous

explanations of its continuing popularity unsatisfactory:

(i) DCA is inefficient regardless of preferences

(ii) It is recommended to investors regardless of market/preferences/expectations.

 A better explanation: DCA is popular because of a specific

and demonstrable cognitive error: investors mistakenly assume that lower average cost means higher profits.

 This explanation makes no unobservable assumptions

about investors or markets. Instead it actually addresses the main argument put forward by DCA’s proponents.

Value Averaging

 Another popular formula investment strategy which (like

DCA) invests gradually.

 Each period the investor must invest whatever new funds

are required to bring portfolio value up to target level.

 VA achieves a higher IRR than plausible alternative

strategies (even in random walk data!)

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Illustration of VA and DCA – Declining Prices

DCA invests a fixed dollar amount ($100). VA invests whatever amount is required to increase the portfolio value by $100 each period. Dollar Cost Averaging (DCA) Value Averaging (VA) Period Price Shares bought Investment ($) Portfolio ($) Shares bought Investment ($) Portfolio ($)

1 1.00 100 100 100 100 100 100 2 0.90 111 100 190 122 110 200 3 0.80 125 100 269 153 122 300 Total 336 300 375 332 Avg.price 0.90 Avg.cost: 0.893 Avg.cost: 0.886

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Illustration of VA and DCA – Rising Prices

Dollar Cost Averaging (DCA) Value Averaging (VA) Period Price Shares bought Investment ($) Portfolio ($) Shares bought Investment ($) Portfolio ($) 1 1.00 100 100 100 100 100 100 2 1.10 91 100 210 82 90 200 3 1.20 83 100 329 68 82 300 Total 274 300 250 272 Avg.price 1.10 Avg.cost: 1.094 Avg.cost: 1.087

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(a) Empirical studies show that VA generally performs worse than investing in one initial lump sum in terms of Sharpe ratio, Treynor ratio, Sortino ratio. (b) VA’s demonstrable advantage: a higher expected IRR than alternative strategies. VA’s popularity suggests investors are more convinced by (b).

21

Quit-Whilst-Ahead Bias

1.1 1.0 0.99 0.9 0.81 1.21 1.1 1.0 0.99 0.9 0.81 Average IRR: 2.4% Average IRR: -0.25%

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(1) (2) (3) (4)

t t t t

a r K K   



) 1 (

1 T t T t t t

IRR K IRR a K ) 1 ( ) 1 (

1

   



 

   

           

T t t t t T t t t

r IRR K IRR K IRR

1 1 1 1

) 1 ( ) 1 (

   

) 1 ( ) 1 ( ) 1 (

1 * 1 1 1

                      

 

     T m t t t t m t t t t

IRR r IRR K a IRR r IRR K The IRR can be regarded as a weighted average of the returns rt, with the weights determined by the PV of the portfolio at the start of each period:

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Hindsight bias in the IRR

 IRR is increased by investing more ahead of strong

returns (good timing)

 IRR also increased by investing more after periods

• f unusually low returns (hindsight bias)

 VA raises the IRR even in simulated random walk data.

This must be entirely due to hindsight bias (this hindsight bias will be seen for any investment strategy which links exposure to the performance to date).

24  Simulations show VA generates a higher IRR, but no

increase in expected profits (driftless random walk).

 Historical data show VA underperforming other strategies.  “Tree analysis” shows that VA is a sub-optimal strategy

regardless of investor risk preferences.

 VA cashflows depend on return in most recent period, so

they are volatile and unpredictable. Edleson (1991) envisages investors holding a ‘side fund’ containing liquid assets sufficient to meet these needs.

 VA gives a negative skew to returns compared to lump

sum (it can lose more than initial investment).

Conclusion: Value Averaging

 VA does not increase expected returns. The high IRR is due

to hindsight bias.

 Invests gradually (inefficient diversification)  Unpredictable cashflows require investors to hold larger

proportion of cash/liquid assets.

 Complex (higher management/transaction/tax costs)  Thus VA is an inefficient strategy. Investors who value

behavioural finance benefits likely to prefer DCA (stable cashflows).

 VA is popular because of cognitive error: investors mistakenly

assume that higher IRR means higher profits.

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References:



“Dollar Cost Averaging – The Role Of Cognitive Bias.” Available at SSRN: http://ssrn.com/abstract=1473046



“Value Averaging and the Automated Bias of Performance Measures.” Available at SSRN: http://ssrn.com/abstract=1606347



Or google “SSRN Simon Hayley”