I have not been able to understand the concept of rebalancing in investing. To me its a form of the gambler’s fallacy. Let:
s_n = stock price at time n
s_{n+1} = stock price at time n+1
Then, if E[s_{n+1}|s_n=c] = c, in my opinion rebalancing does not make any sense
However, if E[s_{n+1}|s_n=c] = E[s_{n+1}] = E[s_n] = k, then rebalancing totally makes sense
Notes:
1. Case 1 is a random walk, case 2 isn’t
2. Case 2 is what I understand as reversion/regression to mean
Comments and thoughts welcome.
Let E[s_{n+1}|s_n=c] = c, but if E[s_{n+1}|s_n,s_{n-1},…,s_{n-m}] ->some constant k as m->infty (call this equation 1) then rebalancing makes sense.Notes:1. The gambler’s fallacy is to believe in equation 1 when in fact it is not true.2. Equation 1 is really regression towards the mean.3. So, if rebalancing really helps in case of the stock market, then in this case maybe the gambler’s hypothesis is true after all.4. What we are saying in above is that although in the immediate short term, stock price is likely to stay at its current value c, in the very long term its price will come down/go up to its intrinsic value k, no matter what the stock history is (do you believe that?). Rationale perhaps being that people will come to their senses.5. Consider E[s_{n+1}|s_n,s_{n-1},…,s_{n-m}] = weighted average of s_n,s_{n-1},…,s_{n-m}. Should you rebalance in this case?