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

(a) DCA Price Shares Cost 1 $3 20 $60 2 $1 60 $60 3 $2 30 $60 110 $180 DCA average cost $1.64 Average price $2.00 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). 4

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.

(a) DCA (b) ESA1 (c) ESA2 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 (a) DCA (b) ESA1 (c) ESA2 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

 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 of investor risk preferences . Terminal Wealth State Price DCA Strategy Rank Density(x81) 480 1 UUUU 16 240 112 0 120 6 UUUD 32 16 144 4 UUDU 32 72 48 0 36 12 UUDD 64 32 192 3 UDUU 32 96 40 0 48 11 UDUD 64 16 72 8 UDDU 64 36 Equities: 16 0 18 15 UDDD 128 Cash: 48 288 2 DUUU 32 144 64 0 72 8 DUUD 64 16 96 7 DUDU 64 48 24 0 24 14 DUDD 128 32 144 4 DDUU 64 72 28 0 36 12 DDUD 128 16 60 10 DDDU 128 30 0 15 16 DDDD 256 12

Total Terminal …A Cheaper Terminal Wealth State Price Wealth Rank Density (x81) Alternative 480.0 1 UUUU 16 224.0 112.0 32.0 144.0 4 UUUD 32 144.0 4 UUDU 32 32.0 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 Lower Cost 16.0 96.0 7 DUDU 64 48.0 29.3 0.0 24.0 14 DUDD 128 120.0 6 DDUU 64 21.3 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 Same Outurns 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!) Illustration of VA and DCA – Declining Prices Dollar Cost Averaging (DCA) Value Averaging (VA) Shares Investment Portfolio Shares Investment Portfolio Period Price bought ($) ($) bought ($) ($) 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 DCA invests a fixed dollar amount ($100). VA invests whatever amount is required to increase the portfolio value by $100 each period. 18

Illustration of VA and DCA – Rising Prices Dollar Cost Averaging (DCA) Value Averaging (VA) Shares Investment Portfolio Shares Investment Portfolio Period Price bought ($) ($) bought ($) ($) 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 19 (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). 20

Quit-Whilst-Ahead Bias 1.21 1.1 1.1 1.0 0.99 1.0 0.99 0.9 0.9 0.81 0.81 Average IRR: 2.4% Average IRR: -0.25% 21    ( 1 ) K K r a  1 (1) t t t t T   a K t  t K 0 (2)   t T ( 1 ) ( 1 ) IRR IRR  t 1 The IRR can be regarded as a weighted average of the returns r t , with the weights determined by the PV of the portfolio at the start of each period:   T T  K   K  t 1   t 1   (3) IRR  r  t   t  t  ( 1 IRR ) ( 1 IRR )   t 1 t 1     * m T  K    K    1    t        ( 1 ) t 1 0 (4)  r IRR  a  r IRR    t t t t  ( 1 )   ( 1 )  IRR IRR    t 1 t m 1 22

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 of 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). 23  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). 24