Upload
hoangnga
View
214
Download
0
Embed Size (px)
Citation preview
Dimitri Vayanos and Pierre-Olivier Weill:A Search-Based Theory of the On-the-Run
Phenomenon
Presented by: Andras Kiss
Economics DepartmentCEU
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
The on-the-run phenomenon
Bonds with almost identical cash-flows trade at different prices(yields)
Just issued (”on-the-run”) bond portfolios have 0.55% lower averagereturn than previously issued (”off-the-run”) bonds with matchedduration (Warga, 1992)
Two potential explanations:1 On-the-run bonds are more liquid2 Repo market loans collateralized by on-the-run bonds offer lower
interest rates (”specialness”)
But why are on-the-run bonds more liquid and more special?
Are liquidity and specialness two independent phenomena?
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Walrasian vs. OTC markets: liquidity and bargaining
One asset, more buyers than sellers
Reservation prices depend on market type: pWb > pW
s , pOb > pO
s
Centralized market (Walrasian auctioneer)
Bertrand-competition, buyers bid up the price: pW = pWb
Sellers take all the surplusNo liquidity issue: ”everyone” can trade instantly
OTC market (no Walrasian auctioneer)
Buyers and sellers meet bilaterally, with frictionsSellers value transactions the same way: pO
s = pWs
Buyers expect positive search cost at future selling date ⇒pO
b < pWb ⇒ pO < pW (”liquidity discount”)
Trade occurs at some price pO ∈[pO
s , pOb
]⇒ pO ≤ pO
b < pW
(”bargaining discount”)Assets are easier to sell if they have more potential buyers, easier tobuy if they have more potential sellers
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Self-fulfilling asymmetric liquidity does not obviously arise
Take two assets with identical cash-flows
OTC market: you can only sell if someone wants to buy, and v.v.
Valuations are such that realized transactions create positive surplus
Asymmetric liquidity would arise along the following lines:
Buyers expect that asset 2 will be harder (costlier) to sell in thefutureThey are unwilling to buy asset 2 if p2 = p1
Sellers of asset 2 are hurt by the difficulty to sell and are willing toreduce the price by ∆p2
Buyers of asset 2 would be hurt the same way in the future (whenthey become sellers)Buyers accept to buy asset 2 if p2 is reduced by at leastPV (∆p2) < ∆p2
⇒ Asset 2 is still traded and equally liquid as asset 1⇒ Expectations of asymmetric liquidity are out of equilibrium⇒ p2 = p1
We need a reason why assets cannot be perfect substitutes for someagents
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Main ideas in the paper
1 Some investors are short-sellers
They initially borrow assets in the repo market from owners and sellthem in the spot marketLater, they buy assets in the spot market and return them to theowner they borrowed the asset fromShort-sellers must return the same asset they borrowed at the end ofthe repo contract
2 Spot markets are over-the-counter
Liquidity is an issueLack of asset substitutability for short-sellers at repurchase time cancreate endogenous liquidity (and price) differences
3 Repo markets are also over-the-counter
Lack of Bertrand-competition among lenders ⇒ positive lending fee⇒ specialness premiumAsymmetric liquidity ⇒ asymmetric specialness premiaRepo market frictions help make the size of price differences(originally caused by spot market frictions) empirically plausible
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Explaining the on-the-run phenomenon
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Centralized (Walrasian) spot market, no shorting
Two assets, issue size S for both
Too many buyers (high valuation agents): Fκ > 2S
Long position’s flow utility: δ + x − y
Long position’s flow cost: rpi
Bertrand-competition: zero surplus for buyers
No short-sales, Walrasian spot market (Proposition 1)
Both assets trade at the same price:
p1 = p2 =δ + x − y
r
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Explaining the on-the-run phenomenon
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
OTC spot market, no shorting
Similar to the ”island-coconut” model of Diamond (1982)
Seller-buyer meetings established at fixed intensity Poisson arrivaltimes
Poisson intensity: λ (search friction)
Measure of sellers: µs
Probability of finding a seller in each instant: λ · µs
Efficient bargaining over the price: transaction occurs if surplus ispositive
Possibly nonzero share of surplus going to buyers: φ ∈ [0, 1]
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Transitions between types (discrete time, intuitive)
λi = λ if buyers accept asset i , and λi = 0 if they don’t
Vb =1
1 + r[λ1µs1 · Vn1 + λ2µs2 · Vn2 + κ · 0 + (1− λ1µs1 − λ2µs2 − κ) · Vb]
Vni =1
1 + r[δ + x − y + κ · Vs i + (1− κ) · Vni ]
Vs i =1
1 + r[δ − y + λiµb · (0 + pi ) + (1− λiµb) · Vs i ]
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Transitions between types (continuous time, exact)
rVb = −κVb +2∑
i=1
λiµs i (Vni − pi − Vb)︸ ︷︷ ︸buyer surplus
rVni = δ + x − y + κ (Vs i − Vni )
rVs i = δ − y + λiµb(pi − Vs i )︸ ︷︷ ︸seller surplus
Total surplus in selling asset i :
Σi ≡ Vni − Vb − Vs i
Surplus division:Vni − pi − Vb = φΣi
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Spot market frictions alone do not displace prices
It turns out:
Σi =x − φ
∑2j=1 λjµs j Σj
(r + κ) + (1− φ)λiµb
Remember:
λi = λ⇔ Σi ≥ 0
In equilibrium, λ1 = λ2 = λ and(Vni ,Vs i , pi , Σi
)are independent of i .
No short sales, search spot market (Proposition 2)
Suppose that short sales are not allowed. In equilibrium, all buyer-sellermeetings result in a trade, and both assets trade at the same price.
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Explaining the on-the-run phenomenon
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Short-selling and repurchase (repo) agreements
Long position: pay the asset price now, receive asset cash-flowduring ownership, receive the asset price at future sale
Short position: receive the asset price now, pay out asset cash-flowduring shorting, pay the asset price at future purchase
Need to borrow the asset for the shorting periodSell it, keep paying the cash-flow to the lender, then buy the assetand return it to the lender
Repo contract (asset-collateralized cash loan):
Lender turns his asset to borrower in exchange for cashDuring the contract, borrower does what he wants with the asset(e.g. shorts it)At maturity, same asset is returned and money is repaid with interest(repo rate)Asset specialness is the discount on its repo rate relative to highestquoted rateAsset specialness ⇔ (flow) lending fee (wi ) paid by borrower
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Walrasian spot and repo markets, short-selling
Frictionless selling, buying, borrowing
Positive lending fee ⇒ all owners want to lend the asset and nobodywants to hold it ⇒ no equilibrium ⇒ lending fee must be zero
Long position’s flow utility: δ + x − y
Long position’s flow cost: rpi
More buyers than sellers ⇒ zero seller surplus
No liquidity issue when short-sellers need to buy the asset back
Short sales allowed, Walrasian spot and repo markets (Proposition 3)
Both assets trade at the same price:
p1 = p2 =δ + x − y
r
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Explaining the on-the-run phenomenon
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Walrasian spot and OTC repo markets, short-selling
ν: repo market search friction (νi = ν if borrowers accept asset iand νi = 0 if they don’t)
Agent types and flow-value equations:¯i : lender (high valuation owner) of asset i , looking for a borrower
rV ¯i = δ + x − y + κ (pi − V ¯i ) + νiµbo (Vni − V ¯i )
ni : high valuation non-searcher in a repo contract (former lender,who has found a borrower)
rVni = δ + x − y + wi + κ (pi − Vni ) + κ (V ¯i − Vni )
bo : low valuation borrower, looking for a lender
rVbo = −κVbo +2∑
i=1
νiµ ¯i (Vni + pi − Vbo)
ni : low valuation non-searcher in a repo contract (former borrower,who has found a lender)
rVni = −δ + x − y − wi + κ (Vbo − pi − Vni ) + κ (−pi − Vni )
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Short-sellers without spot search do not displace prices
It turns out:
(r + κ+ κ) Σi = x + x − 2y − (1− θ)2∑
j=1
νjµ ¯jΣj
Remember:
νi = ν ⇔ Σi ≥ 0
In equilibrium, ν1 = ν2 = ν and(V ¯i ,Vni ,Vni , pi ,wi ,Σi
)are all
independent of i .
Short sales, Walrasian spot, search repo market (Proposition 4)
In equilibrium, both assets trade at the same price and carry the samepositive lending fee.
Symmetric positive lending fee (specialness) due to repo marketbargaining (θ ≥ 0).
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Explaining the on-the-run phenomenon
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Full model (OTC spot + OTC repo + shorting)
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Solving the model
Inflow-outflow equations for types (steady state):
b : F = κµb +2∑
i=1
λ(µs i + µsi
)µb
Market clearing:µ ¯i + µs i + µsi = S
µnsi + µnni + µnbi = µsi + µni + µbi
Flow-value equations:
b : rVb = −κVb +2∑
i=1
λ(µs i + µsi
)(V ¯i − pi − Vb)
In general, only numerical solutions
Closed-form solutions for ”small” search frictions (in the limit)
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Arbitrage
Identical cash-flows, different prices: arbitrage opportunity?
Buy asset 2 and short asset 1:
Benefit: p1 − p2 > 0Cost (of shorting): w1
r
p1 exceeds p2 due to the liquidity and bargaining discounts(”liquidity premium”) and the specialness premiumSpecialness premium is only a fraction of the lending cost, sincecontinuous lending is not assured (market frictions)With a large enough lending fee, w1
r> p1 − p2 and arbitrage is
unprofitable
Opposite strategy can also be unprofitable
For certain (calibrationally plausible) parameter values, the pricedifferences are robust to the presence of arbitrageurs
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Equilibrium selection
Why do short-sellers systematically concentrate in on-the-run bonds?
”Effective issue size” is smaller for off-the-run bonds (buy-and-holdinvestors)
Theoretically, if asset supplies differ (S1 > S2), as search frictionsbecome small:
Short-selling can always be concentrated in asset 1Short-selling can only be concentrated in asset 2 if S1 − S2 is not toolargeSymmetric short-selling of both assets vanishes
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
Explaining the on-the-run phenomenon
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon
App. 1: All inflow-outflow equations
Vayanos-Weill A Search-Based Theory of the On-the-Run Phenomenon