I recently read a Dimensional study* by the same name. “What if we could construct a strategy with a correlation close to 1 with a perfect market timing strategy? Can we estimate what its returns would have been? Can we use these estimates to understand what the market would have “charged” for a perfect market timing strategy?”
“To answer these questions, first let’s define what a perfect market timing strategy needs to know and what it is. A perfect market timing strategy needs to know, with certainty, the future returns of the assets that are eligible for investment. Armed with this information, the perfect market timing strategy always chooses the highest returning asset to invest in.”
Below are further extracted quotes from the longer paper:
“The challenge here is obvious. How can we know with certainty what the future returns on any asset class
will be? Without that knowledge, there is no way to create a perfect market timing strategy. Or is there?
Merton  (1981) shows how to create a strategy that has an almost perfect correlation with the perfect market timing strategy. In particular, this equity strategy buys one share of stock and a one-month put option with a strike price equal to the current stock price adjusted for the yield on the one-month T-bill. We refer to it as a protected equity strategy. In the absence of costs, the payoffs from the protected equity strategy are identical to the perfect market timing strategy.
In the absence of costs, the hypothetical returns and wealth generated by the equivalent perfect market timing
and protected equity investment strategies are astonishing.
So while the perfect market timing strategy has an average monthly return of 2.32%, the net of cost monthly return of the downside protected equity investment is 0.69% per month, which is smaller than the average monthly return of the S&P 500 Index’s 0.93% per month. Hypothetical growth of $100 turns out to be
just $6,086 after costs, much less than the value of $100 invested in the S&P 500 Index ($18,273).  
It turns out that while this is possible, the cost of implementing would have resulted in inferior performance (in terms of ending wealth) [my emphasis] to just holding the S&P 500 Index. If volatility and maximum drawdowns are something an investor is particularly concerned with, a balanced portfolio may be a more cost effective way to achieve this goal. ”
Moral of the story: The paper goes through a number of calculations to demonstrate the cost of perfect market timing, IF such a thing were possible (knowing ahead of time what was going to have the greatest return and when). Since it is not possible to know in advance what and when different investments may perform better than others, the mathematics of diversification helps one get returns when they happen and also when they don’t. One won’t have the best returns all the time, but one also won’t have the worst returns all the time too. One would have a weighted average of the returns over time commensurate with the level of risk one desires.
 Merton, R. C. 1981. “On Market Timing and Investment Performance. I. An Equilibrium Theory of Value for Market Forecasts.” Journal of Business, 1981, Vol. 54, No. 3.folio may be a more cost effective way to achieve this goal.
 By using actual trailing volatility of 60 previous daily returns, we are following a standard methodology similar to Merton (1981), which uses the volatility of 12 previous monthly returns. However, we note that the market prices of options on average tend to reflect a higher implied level of volatility than the actual realized equity volatility. This would cause our cost estimates to be conservative.
 Past performance is no guarantee of future results. It is not possible to invest directly in an index.
 Data Source: S&P 500 Total Return (TR) Index from CRSP Value-Weighted Universe (1962–1988) and S&P 500 TR Index from Bloomberg (1988–2014); One-Month US Treasury Bills from Morningstar. Past performance is not a guarantee of future results. It is not possible to invest directly in an index. Simulated strategy returns based on a model/back-tested simulation. This is not a strategy managed by Dimensional. The performance was achieved with the retroactive application of a model designed with the benefit of hindsight; it does not represent actual investment performance. Back-tested model performance is hypothetical (it does not reflect trading in actual accounts) and is provided for informational purposes only. The securities held in the model may differ significantly from those held in client accounts. Model performance may not reflect the impact that economic and market factors might have had on the advisor’s decision making if the advisor were actually managing client money. This strategy was not available for investment in the time periods depicted. Actual management of this type of simulated strategy may result in lower returns than the back-tested results achieved with the benefit of hindsight. Past performance (including hypothetical past performance) does not guarantee future or actual results. The simulated performance shown is “gross performance,” which includes the reinvestment of dividends but does not reflect the deduction of investment advisory fees and other expenses.
* Purely Academic, September 2015, by Stanley W. Black, Vice President Dimensional Fund Advisors and Samuel Wang, Researcher Dimensional Fund Advisors