Market-beta, momentum, and 1-month-reversal are statistics computed from historical stock-returns. However, when a stock has experienced unusually noisy rates of return (e.g., a rare extreme stock return), ignoring this noise should yield a better estimate of the future statistic than the actual historical statistic. The standard method to do this, at least in the context of market-betas, is Stein shrinkage (vasicek:1973). Our paper exploits the wedge between the two statistics: If investors care about the forward-looking aspect of a measure, then it is the shrunk statistic that should predict future stock returns. If investors care about the backward-looking "characteristics" aspect of a measure, then it is the unshrunk actual historical statistic that should predict future stock returns. We find: [1] Market-beta contains a backward-looking aspect that has a negative influence on future stock returns. This distorts the positive signal in the forward-looking (likely hedging-related) aspect of market-beta. [2] 2-to-13 month momentum is principally a forward-looking effect. [3] The 1-month return reversal effect arises principally from some backward-looking characteristic.