Portfolio Construction: Convexity complexities

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Buying absolute return or tail-risk insurance strategies complicates the portfolio rebalancing process. But Martin Steward finds that a solvency management framework can re-impose some objectivity on that process

We live in an uncertain world. For investors, that is the rationale behind portfolio diversification. In its simplest form, that means taking two negatively-correlated risks and weighting their contribution to a portfolio's risk equally.

At first glance, that seems an odd way to try and make money. The portfolio's exposure to risk is zero, and without risk there can be no return. But that is true only at the beginning of day one. Unless the return to both risks by the end of day one is the same, that risk-neutral position does not persist. If you start with €100 in bonds and €100 in equities, and at the end of day one bonds are down 2% and equities up 2%, you start day two with €98 in bonds and €102 in equities. The portfolio's value has not changed but its exposure (delta) to equities has gone positive. If equities go up 2% and bonds go down 2% again, the portfolio's value at the end of day two is €200.08.

This progressive tilting towards the risk enjoying positive momentum is ‘convexity' - the rate of return from that risk gets higher and higher just as the rate of loss from the other risk gets lower. Option traders call this ‘gamma', a form of value that continues to grow until market momentum reverses. Losses from that reversal are what rebalancing is supposed to prevent: if at the end of day two with €200.08 we sell €4 of equities and buy €4 of bonds, we start day three balanced again, with €100.04 exposed to each risk. Option traders call this re-hedging of delta or banking of profits ‘gamma-trading'.

Why all the options-speak? Partly because options can deliver a particularly aggressive form of this convexity which we will turn to later on, but initially it is to make the point that this process going on at the top level of your portfolio might also be going on at the level of its individual constituents - unless you really do have a simple portfolio of equities and bonds. Volatility funds or convertible bonds carry options; global macro and managed futures funds create option-like exposures. But leaving hedge funds aside, remember this is essentially about hybridity - different risks packaged up together. Do you have multi-asset investment mandates? Corporate bonds delivering both credit and interest-rate risk? The fact that many pension funds have bought large amounts of credit exposure and some have been buying options or option-like strategies as insurance against ‘tail risk' raises an important question: should rebalancing happen at the level of those strategies, or be restricted to the whole-portfolio level so that we are always clear about our net delta to market risk?

"A huge issue right now is clients coming up with multi-asset approaches," says Alan Dorsey, head of investment strategy and risk at Neuberger Berman. "Pre-packaged bundles of securities like that do not sit well with old-fashioned strategic asset allocation. Clients are also implementing convex exposures without trying to reconcile them to the very vanilla asset classes they have."

Blue Diamond Asset Management's flagship multi-asset fund pursues a dynamic asset allocation strategy based on the belief that asset prices mean revert to their fundamental fair values over time and that the most important decision concerns portfolio-level asset allocation. "There's no point seeking implementation alpha if the asset class itself is expensive," as CIO Alex Orus puts it.

But when is the investment grade corporate bond universe ‘expensive'? When the credit risk premium is at its lowest, interest rate risk premium is likely to be at its highest.
"If we liked bonds because interest rates were cheap there'd be no point implementing that with credit bonds - we can do it more efficiently with government bonds or swaps," says Blue Diamond portfolio manager Jonas Andersen. "Similarly if we like credit spreads but regard government bond yields as risky, then we would take that second risk out and purify the credit exposure."

In other words, Blue Diamond actively separates constituent risks in order to concentrate re-balancing at whole-portfolio level.

Mirko Cardinale, asset allocation specialist at Aviva Investors, is more relaxed about this hybridity. "We would typically leave the duration decision to the implementation level, with flexibility against a strategic benchmark," he says. "But it certainly makes sense to swap out unwanted interest rate risk if you are working in a liability-constrained environment and want to maintain a duration match."

Why? Because the more duration is being matched with an LDI programme, the more any marginal contribution to duration from a credit portfolio counts. Your bonds manager could be managing to an absolute return or an index benchmark, as SSgA's head of LDI Raymond Haines puts it: "But that doesn't necessarily agree with the aims at the whole-scheme level, which is why the ultimate decision about exposure to credit or interest rates should rest with whoever is controlling the scheme's glidepath."

But an unconstrained credit mandate can be (almost) pure credit or an (almost) pure duration, and rebalancing between these two risks at the strategy level, as with any multi-risk absolute return strategy, can appear to obviate the need for rebalancing at the whole-portfolio level. As a result, it is tempting to think of the absolute-return strategy and whole-portfolio re-balancing as separate, unrelated processes.

That does not make sense. What is the point of absolute return strategies, if not to limit the whole portfolio's exposure to destructive ‘tail events'? At this point, the absolute return strategy goes from non-correlated to negatively-correlated with the portfolio's other assets, its relative size in the portfolio shoots up, and it is suddenly brought back into the scope of whole-portfolio level rebalancing. Moreover, such an event does more than just change the location of rebalancing responsibility: we must also recognise that the reason it does so - a sudden and extreme realisation of ‘gamma value' - takes us well outside the norms, and usefulness, of standard ‘calendar-based' and ‘tolerance-band' rebalancing processes.

"You are deciding to rebalance because the market has moved a certain amount and it doesn't matter what timeframe that has happened over - the only thing that's important is your forward-looking outlook from that point," says Keith Guthrie, Cardano's UK head of investment management. "If your expected return on equities was 5%, is it now 8% because they have lost 20% of their value? When we describe our approach as ‘dynamic' that's what we mean - we have a view on the opportunity set the market is giving us at any given point."

Making these judgements is what ‘tolerance-band' approaches to portfolio rebalancing is supposed to obviate: if, over time, the convexity of your balanced portfolio had generated a ‘gamma value' of 15%, say, that would trigger rebalancing. But the scale of the market moves associated with ‘tail events' and the strategies designed to insure against them make these relatively tight tolerance bands and long timeframes irrelevant, even as they create a pressing need to bring rebalancing responsibility back up to the whole-portfolio level.

"A number of pension funds have wanted us to tailor exposure to balance another part of their portfolio - and they would rebalance to it or away from it and tell us not to change the amount of delta that we are short," says Keith DeCarlucci, a principal at StormHarbour Alternative Investments who manages long-convexity option strategies. That sort of unhedged or lightly-hedged long-convexity position would usually be bought as downside protection for equity holdings - creating the combination of negatively-correlated risks ( long equity, short equity) that can be rebalanced at the whole-portfolio level - and DeCarlucci says that it would have returned more than 200% during 2008. "But if you are buying what we offer as a product, we've always engineered the strategy so that we would be hedging and clients wouldn't have to rebalance."

But even DeCarlucci's standard delta-hedged, gamma-trading strategy generates a scale of value during tail events that inevitably pushes those decisions back to whole-portfolio level - it might not have been up 200% in 2008, but it did deliver 66%. If you bought and scaled the fund position specifically to hedge tail risk to your equities we'd have to assume that a 66% return would materially affect your whole-portfolio delta, forcing you into market-timing decisions normally delegated to traders.

Let's imagine an equity market crash of 30%. Your equities are down 30%; your option's delta hedge is also down 30%; but the option itself would have moved far into the money - rising some multiple of 30% depending on its individual characteristics. Let's assume the value of the put option now covers the losses suffered in the whole-portfolio equity position and the delta hedge (thanks to its convexity). The value of your portfolio has not moved at all. What has moved - massively - is its equity delta. Its long-equity positions are 30% smaller and its short-equity put position much larger than they were.

You can decide to retain the rebalancing responsibility simply by redeeming from the options manager and buying back into equities. But then you must decide on the timing and scale of that move - do you want to return to neutral delta, delta-positive in the belief that equities are now undervalued, or delta-negative in case of another leg down? This is a difficult decision to make in the midst of a crisis, and one that cannot really be delegated. The options manager could sell his put, buy equities, and re-hedge with a new put, banking the gamma value, hedging against a rebound in equities and restoring his strategy to a delta-neutral position. But that has created a delta-positive position at whole-portfolio level. Is that what you want as the controller of your scheme's ‘glidepath', to recall Haines's words?

Indeed, ‘glidepath' may be the key. Moving this decision away from pure market-timing and back into a systematic framework depends, not on the calendar or tolerance-bands, but on recognising that your scheme is not an absolute-return strategy but a strategy whose risks can be defined relative to a solvency or funding ratio.

"A lot of pension funds now see the need to re-think their rebalancing policy," says Derick Le Roux, head of strategic advice at ING Investment Management. "First, we suggest looking at reframing it around actual exposures, but also risk relative to liabilities and overall financial position."

That moves us into dynamic risk allocation, with triggers for re-allocation within the return portfolio, but also between the matching and return portfolios, with the solvency ratio to some extent defining risk appetite. That helps re-introduce objective limits around the need to re-hedge delta after big moves: market-level triggers are not about timing or forecasting markets, but about defining the terms of action once markets have brought funding levels to a certain point.

"When we first start talking about triggers, clients often ask us: ‘OK, where do you think real yields will be in three years' time?'" explains Steve Aukett, Insight Investments' head of solutions design. "We don't know. But we do know that if rates move up by 1% the scheme would be better funded and therefore ready to take risk off the table. So why don't we embed that expectation about varying appetite for risk into the liability-matching strategy, rather than crystal-ball gazing?"

This whole-scheme (rather than whole-portfolio) view completely changes the dynamic of decision-making around re-hedging after big delta moves, revealing how well-balanced your risks are and providing tight tolerance bands (particularly on funding-ratio downside) to use as triggers for re-hedging delta. These triggers have only to be defined in advance - just as the trigger for de-risking when bond yields hit such-and-such a level is defined in a dynamic LDI programme. The systematic funding or solvency ratio management framework helps solve the rebalancing challenges that tail-risk insurance strategies present to the portfolio manager.

There is a long way to go to that goal. "There has not been an appreciation that there should be an agreed strategy in the event of tail risk being realised," concedes Aukett. "It's rare to find investors preparing for tail events," says Frank Nielsen, head of applied research at MSCI. "It's even rarer to find them knowing what they would do in terms of rebalancing policy when those events happen. What people are concerned about in those situations is how to survive."

But if you have prepared for the worst by implementing these positions, why not define your plans for those positions in the event that the worst happens? Who buys a lottery ticket without also thinking about how they would collect their winnings or spend their windfall? It's time for those who have implemented these positions to start making their wish lists.


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