Case 052Strategy evaluation and backtestsCore

A signal has an information coefficient of 0.06 at one day, 0.045 at five days and 0.03 at twenty days. Cross-sectional daily volatility is 2% and a full rebalance costs 20 bps round trip. Should you rebalance daily or weekly?

The situation

Lohitavan Capital has a cross-sectional equity signal. Its information coefficientThe correlation between a signal's forecast today and the returns that follow, measured across stocks. An IC of 0.05 is considered useful. with the next day's stock returns is 0.06. Measured against the next five days' returns it is 0.045, and against the next twenty days' returns it is 0.03. The typical spread of daily returns across stocks, the cross-sectional volatility, is 2%.

The book is long-short with weights proportional to the signal. Turning the whole book over to fresh signal weights costs 20 bps of gross exposure round trip, spread plus impact. The portfolio manager wants to choose between rebalancing every day and once a week.

Your task

Estimate the gross edge and the cost per year at each frequency, choose one, and say what the numbers imply about the frequency the signal really wants.

Quick check

The one-day IC is the highest. Does that make daily rebalancing the better choice?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Weekly beats daily, but only just breaks even, so the numbers argue for trading even more slowly or more cheaply. A rebalance earns roughly IC times the cross-sectional volatility over the holding period: 12 bps for a day, 20.1 bps for a week, 26.8 bps for twenty days. Against 20 bps a rebalance, daily loses about 20% a year of gross exposure, weekly nets about zero, and a twenty-day rebalance nets about 0.9%.

Step 1How do you turn an information coefficient into an edge in basis points?

Think of a weather forecaster whose rain calls are only slightly better than a coin. For a single day the forecast barely matters, but a shopkeeper stocking umbrellas across a whole season can still profit from it, as long as restocking the shelves does not cost more than the forecast earns. For a book with weights proportional to the signal, each rebalance earns roughly the IC times the cross-sectional volatility over the holding period. Over one day that is 0.06 x 2% = 12 bps. Over five days, volatility grows with the square root of time, 2% x 2.24 = 4.47%, so the edge is 0.045 x 4.47% = 20.1 bps. Over twenty days it is 0.03 x 8.94% = 26.8 bps. The scaling is a rule of thumb, but the same factor applies at every frequency, so the comparison holds.

Lohitavan's IC falls from 0.060 at one day to 0.030 at twenty days, yet one rebalance held for longer earns more before costs, 12.0 bps daily against 20.1 weekly and 26.8 every twenty days, because volatility over the holding period grows with its square root.

Step 2What does each frequency earn and pay over a year?

Multiply by the number of rebalances in a 250-day year. Daily trading earns 12 bps 250 times, 30% a year, but pays 20 bps 250 times, 50%, so it loses about 20% of gross exposure a year. Weekly earns 10.06% and pays 10.00%, a net of about 0.06%, which is zero within any honest error. The twenty-day rebalance earns 3.35% and pays 2.50%, netting 0.85%.

Rebalance	IC	Edge a rebalance, bps	Rebalances a year	Gross a year	Cost a year	Net a year
Daily	0.060	12.0	250.0	30.00%	50.00%	-20.00%
Weekly	0.045	20.1	50.0	10.06%	10.00%	0.06%
Every 20 days	0.030	26.8	12.5	3.35%	2.50%	0.85%

Per unit of gross exposure and before financing, daily rebalancing nets -20.00% a year, weekly nets +0.06% and a twenty-day rebalance nets +0.85%, because the cost of 20 bps a rebalance is paid far more often at the faster speeds.

Daily rebalancing earns 30.0% a year of gross edge but pays 50.0% in costs; weekly earns 10.1% against 10.0%; every twenty days earns 3.4% against 2.5%, the only speed with a clearly positive net.

Step 3So which frequency does the signal really want?

Look at the edge per day held instead of per rebalance: 12.0 bps daily, 4.0 bps weekly, 1.3 bps over twenty days. Fast decay means most of the signal's value is in the first day, which argues for trading fast, but only while the cost of each trade is below what that trade earns. Here it is not. Choose weekly over daily, and tell the portfolio manager the numbers point further: test the twenty-day rebalance, and work on cost. A daily rebalance becomes worthwhile only if a round trip costs less than 12 bps, or if you trade part of the way toward the new weights each day, paying for the changes in the signal rather than for a full turnover.

Say the limitation out loud. The ICs are estimates, and a net of 0.06% a year is well inside their error, so weekly is not a finding of profit, only a finding of not losing. The decision that survives the error is the ranking: slower beats faster at this cost.

Where candidates lose it

Candidates see the highest IC at one day and pick daily rebalancing without converting correlation into basis points or counting how often the cost is paid. A strong signal that is expensive to trade can lose money at its best horizon.

The second miss is comparing ICs across horizons as if they were per-day numbers. An IC of 0.03 on a twenty-day return is measured against a return about 4.5 times as volatile as a daily one, so it earns more per trade, not less.

What the interviewer asks next

What round-trip cost would make daily rebalancing break even?
How would partial rebalancing toward the target weights change the daily numbers?
The ICs were estimated on 500 days. Roughly how uncertain is the 0.06?

Company names and figures are illustrative.