Illiquid Asset Investing 1. Liquidating Harvard

Andrew Ang Illiquid Asset Investing Asset Management
process only involves averaging returns for this period and the past period, then we can filter the
observed returns to estimate the true returns, r t , from observed returns,
1 * *
rt rt rt
1.
1 1
14
*
r t , using:
Equation (2) unsmooths the observed returns. If our assumption on the transfer function is right,
the observed returns implied by equation (2) should have zero autocorrelation. Thus, the filter
takes an autocorrelated series of observed returns and produces true returns that are close to
I.I.D. Note that the variance of the true returns is higher than the observed returns:
1
1
var( rt)
2
2
* *
var( rt ) var(
rt
),
since | | 1,
so we are adding variance to the observed returns to produce estimates of the true
returns.
The unsmoothing process has several important properties:
1. Unsmoothing only affects risk estimates and not expected returns.
Intuitively, estimates of the mean require only the first and last price observation (with
dividends take “total prices” which count reinvested dividends). 11 In Figure 2, we can see
that the first and last observations are unchanged by infrequent sampling; thus
unsmoothing only changes the volatility estimates.
2. Unsmoothing has no effect if the observed returns are uncorrelated.
11
Technically taking means of both the right- and left-sides in equation (2) results in the same means in large
samples.
(1.2)
(1.3)