Analytical Portfolio Projections

AllocationADVISOR uses the formulas presented in de La Grandville 1998 to make projections and determine probabilities. Projections can be made for any of the efficient frontier mixes the Active Portfolio, and the Current Portfolio. AllocationADVISOR’s analytic portfolio projections do not allow for cash flows. When a portfolio is subject to cash flows, use Monte Carlo simulation to project its future value.

Expected Return (Annualized)

The Expected Return (Annualized) is the annual Portfolio Return adjusted for variance drain over T periods. For periods longer than one year, the Expected Return is less than the annual Portfolio Return.

where:

Expected Return
E[R] = Portfolio Return
V = variance of portfolio
T = number of periods

Expected Risk (Standard Deviation)

The Expected Risk is the standard deviation of the Expected Return. As the time horizon increases, the Expected Risk moves towards zero.

where:

Expected Risk
Expected Return
E[R] = Portfolio Return
V = variance of portfolio
T = number of periods

Expected Cumulative Return

The Expected Cumulative Return is the Expected Return compounded over T periods.

where:

Expected Cumulative Return
Expected Return
T = number of periods

Expected Cumulative Value

The Expected Cumulative Value is the portfolio value in period T.

where:

Expected Cumulative Value
Expected Cumulative Return
T = number of periods

Best / Worst Case Return (Annualized)

The Best / Worst Case Return (Annualized) is the annualized return after T periods under a best / worst case scenario. The likelihood of experiencing a return that is more extreme than the Best / Worst Case Return (given the inputs) is approximately 2.5%.

where:

CCM = expected continuously compounded mean return

CCV = expected continuously compounded variance of return

E[R] = Portfolio Return
V = variance of portfolio
T = number of periods

Note: The "1.96" can be replaced with "2." The 1.96 represents 1.96 standard deviations, which corresponds to 95% of the distribution. The 2 represents 2 standard deviations, which corresponds to 95.4% of the standard deviation.

Best / Worst Case Cumulative Return

The Best / Worst Case Cumulative Return is the best / worst case total portfolio return after T periods under a best / worst case scenario. The likelihood of experiencing a total portfolio return that is more extreme than the Best / Worst Case Cumulative Return (given the inputs) is approximately 2.5%.

where:

CCM = expected continuously compounded mean return

CCV = expected continuously compounded variance of return

E[R] = Portfolio Return
V = variance of portfolio
T = number of periods

Note: The "1.96" can be replaced with "2." The 1.96 represents 1.96 standard deviations, which corresponds to 95% of the distribution. The 2 represents 2 standard deviations, which corresponds to 95.4% of the standard deviation.

Best / Worst Case Cumulative Value

The Best / Worst Case Cumulative Value is the best / worst case total portfolio value after T periods under a best / worst case scenario. The likelihood of obtaining a total portfolio value that is more extreme than the Best / Worst Case Cumulative Value (given the inputs) is approximately 2.5%.

where:

CCM = expected continuously compounded mean return

CCV = expected continuously compounded variance of return

E[R] = Portfolio Return
V = variance of portfolio
T = number of periods

Note: The "1.96" can be replaced with "2." The 1.96 represents 1.96 standard deviations, which corresponds to 95% of the distribution. The 2 represents 2 standard deviations, which corresponds to 95.4% of the standard deviation.

Probability of Target Return

Probability of Target Return shows the probability of reaching the Target Return for each portfolio over the selected time periods.

where:

Standard normal cumulative distribution
TR = target return
CCM = expected continuously compounded mean return

CCV = expected continuously compounded variance of return

E[R] = Portfolio Return
V = variance of portfolio
T = number of periods

Probability of Negative Return

Probability of Negative Return shows the probability of receiving a negative return for each portfolio over the selected time periods.

where:

Standard normal cumulative distribution
CCM = expected continuously compounded mean return

CCV = expected continuously compounded variance of return

E[R] = Portfolio Return
V = variance of portfolio
T = number of periods