managing risk of db plans

8/8/2019 Managing Risk of DB Plans

http://slidepdf.com/reader/full/managing-risk-of-db-plans 1/9

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Presentation part 2

Managing risk of DB plans

S. Kourdoupalos



2

Assets

• Two asset classes

1. Risk free assets (bonds)

Portfolio value B, return r B (yield to maturity)

2. Risky assets (stocks)

Portfolio value S, return r S ~ N[E(r),σ]

• Total assets A=B+S,

total return r A=wBr B+wSE(r)



3

Liability

1. The liability L0 is known at t=0

2. But it is not known how it will evolve

3. Suppose the increase rate of the liabilityis r L=r f +DL(Δr)+IL(Δi)+αL

4. Thus, the liability at a future time t is

Lt

=L0

(1+r L

)

t

Note: We will assume in our analysis a one period problem, which

means t=1, as the parameters determining r L change each period

and the hedge needs to be adjusted periodically.



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Hedging conditions

• The conditions to hedge a liability are:

1. (At least) same value at time t

At=Lt A0(1+r A)t=L0(1+r L)t

2. Same duration DA=DL

3. Same inflation sensitivity IA=IL

Only a risk free portfolio (bonds) canfulfill the conditions. Thus, A0=B0

⇒



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Fully funded plan allocation

E(r)

Efficient frontier of risky assets

r L

r B=r L

Fully fundedallocation line

ExpectedSurplus-r L

0

Hedgingportfolio

E(r)-r L

E(r)+za/2

σ-r L

E(r)-za/2

σ-r L

σ



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The hedging portfolio

• Suppose the bond portfolio consists of i

bonds (i=1,2,...,k) described by a column

vector ui=(r i, Di, Ii)΄

• The three hedging conditions summarised:

uB=uL [u1, u2, ..., uk]w=uL

• Where w is the column vector of weights

of each bond in the portfolio

• k unknown weights for 3+1 equations

SOLUTION??

⇒



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Under funded plan allocation

E(r)

Efficient frontier of risky assets

r L

Under fundedallocation line

Under fundedexpected surplus

-r L

0

r L

r B

E(r)-za/2

σ-r L

E(r)+za/2

σ-r L

E(r)-r L

(1+r L)(L0-B0)/B0

Hedgingportfolios

σ

Fully hedged with

100(1-a/2)%confidence



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Various

1. Even though hedged, an increase of the

liability L0(1+r L)t means paying more, i.e. extra

cost

Sponsors can negotiate L0 to reduce the cost

2. If sponsors were able to achieve positive

alpha, i.e. abnormal returns, through activeportfolio management, they should have been

running a hedge fund not a pension plan.

Passive portfolio management

managing risk of db plans

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