Surplus Optimization

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Exhibit 31 in Reading 17 indicates that surplus optimization can be run for any funded ratio. However, if the liability stream is underfunded, there is no surplus. Therefore, how can an MVO approach be applied to surplus assets if there is no surplus. Am I missing something here? Thanks.
 
I just did this reading last night so I may not have the depth in my answer you’re looking for. But no as far as I know a surplus optimiation can’t be done if underfunded. By virtue of the name, if there is no surplus there’s nothing to optimize, in which case you’d have to use another LR approach like hedging/return seeking approach. Perhaps they mean it can be applied to any funding ratio above 1? If I’m wrong I’d love to hear the correct answer as well!
 
I do not agree with StageRight, maybe someone can confirm my thoughts below ?
The Surplus Optimization can be use for a negative surplus or a positive surplus.
If you have a negative surplus, you can still optimize it i.e. get a lower/greater volatility of that negative surplus.
 
It’s so dumb and confusing, but BearFlag is correct. There’s a chart on Page 287 that notes that the Surplus Optimization and Integrated Asset-Liability approaches can be used under any funded ratio. The Hedged approach needs a surplus.
BearFlag, can you elaborate on what a negative surplus is? I’m assuming its just an underfunded plan, but that terminology is confusing.
 
Plan assets - liabilities = surplus
Negative surplus is called a deficit. Positive surplus is just called surplus.
 
It’s called “Surplus Optimization” but you should read it “Assets - Liabilities Optimization”. The curriculum provides a good example in which it shows you that liabilities are listed together with the other assets, and more precisely it is the PV of liabilities, and you treat it as if it were a short position. You run your MVO as for a long-short fund strategy.
So, when you run your MVO, in the vector of returns, you include the E(r) for the “asset” called PV(liabilities). And in you covariance matrix, you include variance and covariances of the ”asset” called PV(liabilities). Then you add a constraint to the allocation weight of PV(liabilities) to be equal to:
wPV(liabilities) = – PV(liabilities) / [Amount invested + PV(liabilities) ]
So if the size of your pension fund is EUR 60K and you estimate the PV of your liabilities to be 40K, then the allocation weight constraint to PV(liabilities) should be – 40%.
This is not the end. You should add another budget constraint:
∑ wi = 100% + wPV(liabilities) = 100% – 40% = 60%
This last constraint is needed otherwise we would have a 140/40 mutual fund portfolio, instead we have just a 100/40 strategy. The extra 40% in the long position is what you would invest using the proceeds from shorting 40% of the portfolio investment amount… but this is not our case.
If you are not familiar with this kind of constraints in MVO, you might wonder if it’s even possible to sum allocation weights to less than 100%. Answer is “Yes”. In a pure neutral strategy (where you go long and short in equal amounts), the budget constraint would be to sum to zero!
Now suppose you have different streams of liabilities with different risk profiles. Same as before, you just add more short positions to your asset allocation.
And again, this is feasible even if you started with a deficit. Just think of this scenario:
  • you have liabilities with E(r) = 5% and PV = USD 100K
  • you have 1 asset, with E(r) = 50%
  • assume both have same volatility as correlation = 1
  • assume time horizon = 1
Just based on this, you see that by investing just USD 70K in the risky asset, you would meet your liability obligations.
 
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