5. Portfolio Revisions
- trading decisions based on expected active return, active risk, & transaction costs
- underestimating transX costs -> frequent trading -> suffering higher than expected transX costs & lower than expected alpha
- as the horizon of the forecast alphas decreases -> returns become noiser with shorter horizons. rebalancing for very short horizons would involve frequent reactions to noise, not signal. But the transaction costs stay the same, whether we are reacting to signal or noise.
- trading decisions based on expected active return, active risk, & transaction costs
- underestimating transX costs -> frequent trading -> suffering higher than expected transX costs & lower than expected alpha
- as the horizon of the forecast alphas decreases -> returns become noiser with shorter horizons. rebalancing for very short horizons would involve frequent reactions to noise, not signal. But the transaction costs stay the same, whether we are reacting to signal or noise.
**individual stock's alpha
e.g.) Boeing's alpha = 0.54%, beta = 0.56, monthly risk-free rate = 0.4%
=> Rj = Rf + beta x (Rm - Rf) = Rf (1 - beta) + beta x Rm
Rf(1 - beta) = 0.4% (1 - 0.56) = 0.18%
0.54% - 0.18% = 0.36% > 0 -> Boeing performed 0.36% better than expected
Annualized Excess Return = (1 - .0036) ^ 12 - 1 = 4.41%
- we can capture the impact of new information, and decide whether to trade, by compaing the marginal contribution to value added for stock n, MCVAn, to the transactions costs. The marginal contribution to value added shows how value added, as measure by risk-adjusted alpha, changes as the holding of the stock is increased with an offsetting decrease in the cash position.
- as our holding in stock n increases, alpha n measures the effect on portfolio alpha
- the change in value added also depends upon the marginal impact on active risk of adding more of stock n, MCARn, which measures the rate at which active risk changes as we add more of stock n
- let PCn be the purchase cost and SCn the sales cost for stock n. The situation before new information arrive is
e.g.) Boeing's alpha = 0.54%, beta = 0.56, monthly risk-free rate = 0.4%
=> Rj = Rf + beta x (Rm - Rf) = Rf (1 - beta) + beta x Rm
Rf(1 - beta) = 0.4% (1 - 0.56) = 0.18%
0.54% - 0.18% = 0.36% > 0 -> Boeing performed 0.36% better than expected
Annualized Excess Return = (1 - .0036) ^ 12 - 1 = 4.41%
- we can capture the impact of new information, and decide whether to trade, by compaing the marginal contribution to value added for stock n, MCVAn, to the transactions costs. The marginal contribution to value added shows how value added, as measure by risk-adjusted alpha, changes as the holding of the stock is increased with an offsetting decrease in the cash position.
- as our holding in stock n increases, alpha n measures the effect on portfolio alpha
- the change in value added also depends upon the marginal impact on active risk of adding more of stock n, MCARn, which measures the rate at which active risk changes as we add more of stock n
- let PCn be the purchase cost and SCn the sales cost for stock n. The situation before new information arrive is
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