Approaches to Liability-Relative Asset Allocation: Surplus Optimization

No. As risk aversion increases, portfolio volatility should decrease.

If you were the top asset manager at UK company Royal Mail Group in March of 2016, you would have been pretty ecstatic, and with great reason. The assets within your pension fund totaled EUR 7,300,000,000, while liabilities were only EUR 3,800,000,000. That's some surplus! But then the question becomes what to do with such a large asset base. For some companies, the goal is to further reduce future contributions. How would Royal Mail Group go about reducing future contributions?

While that may sound complicated, the steps of surplus optimization break out the exact process. To start, you'll need to set asset classes and determine the time horizon, which is typically one year. This step is where you'll apply any volatility constraints to the expected returns. For example, a company may prefer to keep volatility of the surplus below 15%. Then, it's time to estimate expected returns and volatilities for the asset classes and estimate liability returns. At this point, your economic projections from historical data, analysis, and judgment are introduced. So what's included in this second step of the surplus optimization?

No. Systematic risks aren't a part of economic projections.

No, actually. Excess risk premiums won't factor in historical data projections.

Yes! Capital market expectations are a part of this second step because they capture the economic data, historical data, and your own personal opinions. So this is where you'd include your own economic forecasts. The next step is where the investor gets involved by establishing constraints on the asset mix, like weighting ranges or no short selling. Then you take the economic forecasts and investor constraints to estimate the correlation matrix and volatilities.

Once the correlation matrix is complete, the surplus efficient frontier can be calculated and compared with the asset-only efficient frontier so that the proper portfolio mix can be chosen. But you'll need to be careful that the proper portfolio mix meets all the constraints of the institutional investor. For example, suppose your current portfolio mix falls below the surplus efficient frontier but above the maximum level of surplus risk for the client. Which portfolio do you think best meets the client's needs?

No. That's not the optimal level of risk for return.

No, actually. This portfolio is well above the level of surplus risk that the client wants to take.

That's not it. Risk aversion impacts the investor's utility.

That's not it. The surplus optimization isn't focused on just returns.

Not quite. Returns per unit of risk are a focus, but that's always going to lead to an efficient frontier portfolio.

Excellent! The surplus optimization is focused on the impact of asset allocation on the surplus. That means that the portfolio mixes will differ from the asset-only approach that's solely focused on returns per unit of risk. This also usually means that bonds are a bigger part of the surplus optimization portfolio.

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Right! You'll want to focus on the portfolio that meets the client's volatility requirement, so that means it may not be the portfolio that falls along the efficient frontier or the optimization asset mix after constraints are factored in. Typically, this also means that the portfolio chosen in the implementation of a surplus optimization will differ from the portfolio mixes of an asset-only approach. Why will the surplus optimization differ from the asset-only approach?

Not quite. That earned interest isn't going to do much to reduce the future contribution values.

No. That's not a good strategy to reduce risk for the beneficiaries of the plan.

Yes! If you're the asset manager at Royal Mail Group, you'd consider earning an extra return on the asset base to reduce the need for future contributions. That's where the __surplus optimization__ asset allocation approach can come in. Surplus optimization is the adaptation of the mean–variance optimization to specifically generate a return on the surplus assets. Essentially, it chooses an asset allocation that maximizes the expected return, less a penalty for surplus return volatility over the chosen time horizon.

Put another way, it applies the utility function equation for individuals to institutional investors. $$\displaystyle U^{LR}_{M} = E(R_{s,m}) - 0.005\lambda\sigma^2(R_{s,m})$$ Here, $$\displaystyle U^{LR}_{M}$$ is the surplus objective function’s expected value for the specified asset mix, _E_(_R__{_s_,_m_}) is the expected surplus return for asset mix _m_, the investor’s risk aversion is λ, and surplus return is defined as $$\displaystyle \frac{\mbox{Change in asset value} - \mbox{Change in liability value}}{\mbox{Initial asset value}}$$.

This equation should look familiar, and it acts just like the individual utility function. So as the risk aversion of the institutional investor increases, how will the penalty for portfolio volatility react?

Exactly! The penalty is represented by the variable that's subtracted from the expected return. So as risk aversion increases, so does the penalty for portfolio volatility. Naturally, this should make sense, as a company doesn't want to take more risk and lose its surplus without generating enough excess returns. Basically, this surplus-optimization approach builds on an assumed relationship between the asset and the liability and uses the natural hedging between the asset and liability as a tool to generate excess returns.

Earn excess investment returns

Invest the surplus in cash to preserve its value

Invest the surplus amount back into the business to earn a return

Systematic risks

Excess risk premiums

Capital market expectations

The current portfolio mix

The portfolio on the efficient frontier

The portfolio that meets the client's volatility target

It's focused on return maximization

It's focused on returns per unit of surplus risk

It's focused on the value of assets less liabilities over the planning horizon

It will increase

It will decrease

There will be no change

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