ABSTRACT

The most common baseline is the Buy-and-Hold (BAH) strategy, in which one invests wealth among the market with an initial portfolio of b1 and holds the portfolio till the end. The manager only buys the assets at the beginning of the first period and does not rebalance in subsequent periods, while the portfolio holdings are implicitly changed following the market fluctuations. In particular, at the end of period t , the portfolio holding becomes bt

⊙ denotes the element-wise product.∗ BAH’s

final cumulative wealth is the initial portfolio-weighted average of individual asset returns, that is,

Sn(BAH(b1)) = b1 · (

)

,

where b · x denotes the inner product bx. The BAH strategy with uniform portfolio b1 =

( 1 m , . . . , 1

) is referred to as the uniform BAH strategy, which is usually adopted

as a market strategy to produce a market index.†

3.2 Best Stock Strategy

Another common benchmark is the Best Stock (Best) strategy, which is a special BAH strategy that invests all capital on the best stock in hindsight. Its initial portfolio b0 can be calculated as, b0 = arg maxb∈m b ·

) , which is thus a hindsight strategy.

The strategy’s final cumulative wealth equals