Ebook Optimal Asset Allocation and Risk Shifting in Money Management
“The real business of money management is not managing money, it is getting money to manage.” Indeed, with the number of mutual funds in the US exceeding the number of stocks, fund managers are increasingly concerned with attracting investors’ money. Recent empirical evidence (e.g., Gruber (1996), Chevalier and Ellison (1997), Sirri and Tufano (1998)), offers simple insight to a manager: new money is expected to flow into the fund if the manager has performed well relative to a certain benchmark. With her compensation typically increasing in the value of assets under management, this positive fund-flows to relative-performance relationship creates an implicit incentive for the manager to increase the likelihood of future fund inflows, distorting her asset allocation choice. There is, of course, also an explicit incentive induced by the manager’s compensation: managing assets in line with her own appetite for risk, which need not coincide with those of fund investors. This is another source of conflict between a fund manager and her investors, originally pointed out by Ross (1973). Together, the manager’s implicit and explicit incentives shape her asset allocation policy. Understanding this policy is of utmost importance to fund investors who may be hurt by adverse incentive effects. Our objective is to examine the implications of these incentives within a familiar dynamic portfolio choice framework.
We consider a dynamic economy and focus on a fund manager, guided by a risk-averse objective. The manager’s compensation depends on the total value of the fund at some terminal date (e.g., end of the year). This fund value is determined by the portfolio choice of the manager during the year and by non market able inflows/outflows of new money at the year-end. The rate of flows into the fund depends on the manager’s performance over the year relative to a benchmark a reference portfolio of stock and money markets. We consider several types of the flow-performance relationship, with the baseline specification being adopted from Chevalier and Ellison. These specifications share the common feature that they all give rise to local convexities in the manager’s objective function. The presence of such local convexities and their importance have been noted by numerous studies. In our analysis, we uncover several novel implications entailed by convexities that are robust across all specifications of the manager’s payoff, and are at odds with conventional views expressed in the literature.
The manager’s optimal policy reflects the interplay between the implicit incentives to boost risk induced by these convexities and her “normal,” absent implicit incentives, policy driven by her attitude towards risk. We find that such a tradeoff gives rise to a “risk-shifting” range over which the manager deviates significantly from her normal policy by taking on additional risk (in line with Jensen and Meckling (1976)). Our analysis, however, identifies two possible directions in which the manager optimally manipulates her risk exposure in this range: by boosting her portfolio volatility or by decreasing it. The latter direction is somewhat unexpected: how can “gambling” to finish ahead of the benchmark be consistent with a decrease in portfolio volatility? Simply, in the context of relative performance evaluation, any strategy entailing a deviation from the benchmark is inherently risky. By taking on more systematic risk than that of the benchmark (boosting portfolio volatility), the manager gambles to improve her relative standing when the benchmark goes up. Similarly, by taking on less systematic risk than that of the benchmark (reducing volatility), the manager bets on improving her relative performance when the benchmark falls. The direction of the manager’s choice of a deviation from the benchmark depends on her risk aversion: a more risk tolerant manager decides to boost volatility, while a relatively risk averse manager does the opposite, despite the positive risk premium offered by the risky asset.
Since the manager is risk averse, the range over which she engages in excessive risk taking, as well as her ensuing risk exposure, are finite. No risk shifting takes place when the manager is considerably behind or ahead of the benchmark, where the flows-induced incentives are weak and the normal policy considerations prevail. Overall, the strength of managerial risk-taking incentives is highly time and state-dependent, with a maximum positioned somewhere deep in the underperformance region and a minimum differing across the specifications of the flow-performance relationship we consider. These implications are typically in disagreement with the predictions of extant work arguing that risk taking is most pronounced next to convex kinks or discontinuities in a manager’s payoff (induced by implicit incentives or explicit compensation contracts; see, e.g., Chevalier and Ellison (1997), Murphy (1999)). In fact, in one of our specifications, we demonstrate that the risk-taking incentives are actually minimized around a discontinuity. These sharp differences in implications are due to the differences in adopted measures of risk taking. The traditional definition of a risk-taking incentive (e.g., standard in corporate finance) is the sensitivity of the manager’s payoff to volatility. This measure captures the strength of the manager’s desire to increase her risk exposure relative to some fixed status quo asset allocation. Our measure of risk taking is the optimal risk exposure as defined in the portfolio choice literature: the fraction of the fund optimally invested in the risky asset. Intuitively, instead of just taking a partial derivative of the manager’s value function with respect to volatility, we take this derivative and equate it to zero to derive the optimal volatility for each level of relative performance.
For most of our analysis we adopt the simplest possible setting, the Black and Scholes (1973) economy with a single source of risk, to convey our most important insights pertaining to managerial risk shifting. To investigate the manager’s portfolio allocation across different stocks and exposure to systematic versus idiosyncratic risk, we extend our baseline model to multiple sources of uncertainty. The overall behavior of the manager is analogous to that in the baseline analysis. However, the manager’s incentive to deviate from the benchmark portfolio when underperforming now manifests itself not in increasing or decreasing the fund’s volatility but in tilting the weight in each risky security away from the benchmark. We also demonstrate that risk shifting does not necessarily involve taking on idiosyncratic risk. Indeed, when faced with both systematic and idiosyncratic risks, the manager may very well optimally expose herself to no idiosyncratic risk, while engaging in her optimal risk shifting via systematic risk only.
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