244 CHAPTER 6. THE MARKET FOR CURRENCY FUTURES
into even deeper sloughs of despond despair when they remember that the calcu-
lated margin is almost surely too optimistic: the real world is never so simple as
our computers assume.- Errors in the regressorIf you use futures data, there is a problem of bid-ask
noise (you would probably like to have the midpoint rate, but the last traded price
is either a bid or an ask—you don’t know which), changing maturities, jumps in
the basis when the data from an expiring short contract are followed by prices from
a 3-month one, and synchronization problems between spot and forward prices.
So if you use futures transaction data there is an errors-in-variables problem that
biases theβestimate towards zero.
Many of these problems can be solved by using forward prices computed from
midpoint spot and money-market rates for the desired maturityT 2 −T 1. - Lead/lag reactions and the intervalling effect Thesektends to stay close
to theeur, from anusdperspective. But this means that, if theeurappreciates,
for example, and thesekdoes not entirely follow during the same period, then
there typically is some catching-up going on in the next period. This means
that the correlation between changes in the Euro and the Krona is not purely
contemporaneous.
This gives rise to theintervalling effect. The beta computed from, say, five-minute
changes is quite low, but the estimates tend to increase if one goes to hourly, daily,
weekly, and monthly intervals. This is because, the longer the interval, the more
of the lagged reaction is captured within the interval.
Example 6.14
Suppose that, “in the long run” every percentage change in theeurmeans an
equal change in thesek’s value, but only three-quarter of that takes place the same
day, with the rest taking place the next day, on average. Then your estimatedγ
from daily data would be more like 0.75 than 1.00 as your computer overlooks the
non-contemporaneous linkages. But if you work with weekly data (five trading
days), then for four of the days the lagged effect is included into the same week
and picked up by the covariance; only 0.25 of the last-day effect is missed, out
of 5 days’ effects, causing a bias of just 0.25/5 = 0.05. Obviously, with monthly
data the problem is even smaller.
The intervalling effect means that, ideally, the interval in your regression should
be equal to your hedging horizon, otherwise the beta tends to be way too low.
This can be implemented in three ways. First, you could takenon-overlapping
holding periods. The problem is that this often leaves you with too few useful
observations. For instance, if your horizonT 2 −T 1 equals three months and you
think that data older than 5 year are no longer relevant, you have just a pitiful
20 quarterly observations. Second, you could useoverlapping observation periods.
For example, you work with 13-week periods, the first covering weeks 1-13, the
next weeks 2-14, etc. This leaves you more useful information; but remember
that the usualR^2 and t-statistics are no longer reliable because of the overlap
created between the observations. (Hansen and Hodrick (1980) show you how