Case 069Strategic and tactical allocationCore

A balanced fund's CIO wants a 5 point equity overweight against a 60/40 benchmark. Equities have 18% volatility, bonds 6%, correlation 0.1, and the tracking error budget is 2%. How much of the budget does the tilt use, and what information ratio does it need to be worth it?

The situation

Yamunotri Balanced Fund is benchmarked to 60% equities and 40% government bonds and has a tracking error budget of 2% a year. The CIO believes equities will beat bonds over the next year and wants to hold 65% equities and 35% bonds, a 5 point overweight funded from bonds.

The risk team's figures: equity volatility 18%, bond volatility 6%, correlation between them 0.1. The stock selection team inside the equity sleeve also uses the tracking error budget, and the board expects the fund's active risk to earn an information ratio of about 0.5 over time.

Your task

How much tracking error does the tilt add, what share of the budget is that, and how much must equities beat bonds for the tilt to be worth its risk?

Quick check

Roughly how much tracking error does the 5 point overweight add?

Worked solution

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

30-second answerThe answer to give first

The tilt adds about 0.92% of tracking error, under half the 2% budget, and about 21% of it measured in variance. The active bet is long 5 points of equity and short 5 of bonds, and that spread has a volatility of about 18.4%. To match an information ratio of 0.5, the tilt must earn about 0.46% a year, which needs equities to beat bonds by about 9.2 points. That is a demanding hurdle for one yearly call.

Step 1How do you compute the tilt's tracking error?

Tracking error is the volatility of the gap between the fund and its benchmark. The gap here is a position of plus 5 points of equity and minus 5 points of bonds, so its volatility is 5% times the volatility of the equity-minus-bond spread. That spread's variance is 18 squared plus 6 squared minus 2 times 0.1 times 18 times 6, which is 338.4; its volatility is 18.40%, and 5% of that is 0.92%. The low correlation means bonds barely offset equity, so the answer is close to the naive 5 times 18, 0.90%, but slightly higher because selling bonds adds a little risk of its own.

The relationship

TE = w\,\sqrt{\sigma_e^2 + \sigma_b^2 - 2\rho\,\sigma_e\sigma_b} = 0.05\sqrt{18^2 + 6^2 - 2(0.1)(18)(6)} \approx 0.92\%

w	the size of the overweight, 5 points
sigma_e, sigma_b	equity and bond volatility, 18% and 6%
rho	their correlation, 0.1

What it says in wordsA tilt from bonds into equities has the volatility of the gap between the two assets, scaled by the size of the tilt.

Step 2What share of the budget does that use?

Two answers, and the second matters more. As a simple share, 0.92% is 46% of 2%. But independent risks add in squares, like the sides of a right-angled triangle, so the tilt uses only 21% of the budget's variance, and 1.78% of tracking error remains for stock selection if the two are unrelated. This is why tactical calls cost less risk than they feel: a 5 point move sounds bold, but it leaves most of the budget to the equity team.

Yamunotri's 5 point equity tilt adds 0.92% of tracking error, 46% of the 2% budget in simple terms but only 21% in variance, leaving 1.78% for independent stock selection.

Step 3What information ratio does the tilt need, and is that realistic?

The information ratioActive return divided by tracking error: how much extra return each unit of active risk earns. Around 0.5 is regarded as good over long periods. is active return over tracking error. To earn 0.5 on 0.92% of risk, the tilt must add about 0.46% a year, and since it is 5 points wide, equities must beat bonds by about 9.2 points over the year. At an information ratio of 0.3 the hurdle is 5.5 points. Grinold's fundamental law explains why this is hard: a single yearly call has a breadth of one, so its information ratio equals the skill of that one call, and few forecasters are right often enough to average 0.5 on one bet a year.

Target information ratio	Tilt must add, % a year	Equities must beat bonds by
0.2	0.18%	3.7 points
0.3	0.28%	5.5 points
0.5	0.46%	9.2 points

For the 5 point tilt to earn an information ratio of 0.5 on its 0.92% of tracking error, equities must beat bonds by about 9.2 points over the year; even 0.2 needs 3.7 points.

So the recommendation is measured. The tilt fits comfortably in the budget, which answers the risk question. Whether it is worth taking is a question about the CIO's record on this kind of call. If the evidence of skill is thin, a smaller tilt, 2 or 3 points, or several smaller calls through the year, gives a better chance of earning its risk. The limitation: volatilities and correlations move, and in a sell-off equity-bond correlation can rise or fall sharply, changing the tilt's risk when it matters most.

Where candidates lose it

The first slip is answering 5%, confusing the size of the tilt with its risk, or 0.9% while forgetting that the bonds sold to fund it add a little risk too.

The second is adding tracking errors linearly: 0.92% plus the stock team's risk cannot exceed 2%. Independent risks add in squares, so the budget has more room than the simple sum suggests, and saying so is what the interviewer is listening for.

What the interviewer asks next

The equity-bond correlation jumps to 0.6 in a sell-off. What is the tilt's tracking error now?
How would you split the 2% budget between the CIO's tilts and stock selection?
How many independent calls a year would the CIO need to make an information ratio of 0.5 plausible?
Would you implement the tilt with index futures or by trading the underlying funds?

Company names and figures are illustrative.