# Help Understanding Surplus Optimization

Really struggling to grasp this concept. Can anyone provide a good explanation to help me understand this? Searched the forums, but haven’t had much luck. Thanks in advance!

Think of mean-variance optimization but substitute:

1. mean portfolio return with surplus return (= asset return - liability return)
2. portfolio standard deviation with surplus risk (std dev of surplus return)

One of the objective of the optimization process is to achieve a target surplus return (say 3%) subject to minimizing surplus risk.

This is a tough topic for me as well, and I’ve yet to see any particularly good explanations that capture the essence of it. I think there are a few errors in the text that seem to compound the difficulty. For example, there’s an errata on page 109, and I’m wondering if there should be an errata for the X axis of Exhibit 28 page 107 or the text above the exhibit that describes the X axis. Is surplus risk on the x-axis of Exhibit 28 p.107 really expressed in money terms as the text above Exhibit 28 notes? If it is, why is there not a dollar sign on the x axis?

A critical piece for understanding this concept seems to be Blue Box 6 question #3 on page 110. The solution points out that as surplus return increases, the allocation to corporate bonds decline. (See Exhibit 29). This is because bond prices and present value of liabilities move together… I guess I really don’t understand why the surplus return is increasing. Let’s say rates are going down–so, contractual liabilities should be going up by the same amount that your bonds (hedging assets) are increasing unless there’s basis risk. Somebody wanna clarify?

The corporate bonds plays the role of a hedge to the pension liabilities. The more corporate bonds the portfolio holds, the more closely that changes in the portfolio return matches the change in the PV of the pension liabilities, resulting in a lower surplus return and a lower surplus risk.

If you refer to Exhibit 29, as we move from (surplus return = \$0.26 bil) to (surplus return = \$0.32 bil):

• the allocation to corporate bonds decline, which implies the pension wants to reduce the allocation put in place to hedge the pension liabilities, and
• the allocation increases for hedge fund, real asset, and real estate; which will generate higher returns for the portfolio (and higher than the change in the PV of the pension liabilities), thus generating a higher surplus return.

As the portfolio allocates less to corporate bonds (the liability-hedging assets) and allocates more to hedge fund, real asset, and real estate (relatively poor liability-hedging assets), the surplus risk then increases.

From what I gather, MVO only considers asset’s returns correlations and standard deviations, surplus optimization considers also considers liability returns correlations and standard deviations.

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I think Surplus Optimization Model tries to calculate the best mix of asset classes (or simply assets) that hedge or cover for liabilities cash outflows and also maximazes sharpe for the residual assets. The model take into account the characteristics of the liabilities the investor want to comply with, so it would be more suitable than MVO Model.

Yes, agree that the surplus optimization model is more appropriate than MVO for institutional investors that have liability relative constraints (e.g. pension funds).

I think the best mix would depend on the investor’s objectives:

• It can be the mix of assets that achieve a specific surplus return while minimizing surplus volatility.
• It can be the mix of assets that minimizes surplus volatility below a certain threshold.

They don’t look at Sharpe ratio. The slope of the frontier measures surplus return/surplus volatility, which is more like Information ratio (with the benchmark being the liability).

To the left of the surplus efficient frontier, the asset mix will contain more hedging assets, hence lower surplus return and lower surplus volatility.

To the right of the surplus efficient frontier, the asset mix will contain less hedging assets, hence higher surplus return and higher surplus volatility.

Thank you @fino_abama

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