Intermediary Funding Cost and Short-Term Risk Premia

Transcription

1 Intermediary Funding Cost and Short-Term Risk Premia Wenhao Li and Jonathan Wallen November 22, 2016 Wenhao Short-Term Risk Premia November 22, / 26

2 Introduction Question: How is short-term risk premium priced? We link this risk premia with intermediary funding cost in a search and bargaining framework. Model implications are tested in equities, bonds, and currencies. Main result: Intermediaries price order imbalances (liquidity shocks) by asset idiosyncratic risks and intermediary leverage. Wenhao Short-Term Risk Premia November 22, / 26

3 An Overview of the Model Liquidity Shock Q Search Buyers l Leverage Risk-Neutral Investors Risk-Neutral Intermediaries Wenhao Short-Term Risk Premia November 22, / 26

4 An Overview of the Model Competitive and Centralized Funding Market Holding Q l Leverage Risk-Neutral Investors Risk-Neutral Intermediaries Wenhao Short-Term Risk Premia November 22, / 26

5 An Overview of the Model l Leverage λ # Search Buyers Holding Q Risk-Neutral Investors Risk-Neutral Intermediaries Wenhao Short-Term Risk Premia November 22, / 26

6 Preview: Equilibrium Price Shock Price Fundamental Value Transaction Date 0 Liquid Shock Day t Expected Change Wenhao Short-Term Risk Premia November 22, / 26

7 Preview: Equilibrium Price Shock Price Fundamental Value 0 Liquid Shock Day t Increase in leverage Expected Change Wenhao Short-Term Risk Premia November 22, / 26

8 Preview: Equilibrium Price Shock Price Fundamental Value 0 Liquid Shock Day t Increase in leverage Expected Change Increase in idiosyncratic volatility Wenhao Short-Term Risk Premia November 22, / 26

9 The Model Setup Continuous time, infinite horizon. Fix a probability space (Ω, F, P). All stochastic processes are adapted. A finite number of assets. Consider a specific asset with fundamental value X t. A continuum of risk-neutral and deep-pocket investors with trading gains π when hit by a liquidity shock. Expected utility of trading at τ when hit by a sell shock at t: u t (Q) = E t [Q(P τ + π X τ )] Throughout the presentation, we consider investors sell shocks. Investors search intermediaries to trade. Wenhao Short-Term Risk Premia November 22, / 26

10 Intermediaries Intermediary i [0, 1] has leverage ξ i, with distribution F ( ). Default probability of intermediary i is ν(ξ i ), which increases in ξ i. Bargain with investors to set price. Offloading imbalance at fundamental value X t, which is a martingale. X t = α t + β t F t + σε t where var(ε t ) = 1, E(ε t ) = 0, and ε t is independent from other processes. Wenhao Short-Term Risk Premia November 22, / 26

11 Funding Market Fully competitive funding market. Margin is set endogenously, given default risk. Fix interest rate r. Set margin m $ Repayment Date Repayment Leverage of Intermediary i Moving fundamental X 9 1 v(ξ 8 ) No Default X $ e &(()$) Constant leverage: ξ 8 v(ξ 8 ) Default min {m $ X $ + X (, X $ e & ()$ } Search time τ for counterpart Figure: Illustration of Funding a Long Position for the Intermediary Wenhao Short-Term Risk Premia November 22, / 26

12 Equilibrium Definition An equilibrium is defined as the searching strategy of investors (leverage threshold l), competitive funding margin m t, and intermediary-investor bargaining price P t, such that Search strategy is the optimal choice of investors. Margin is set to the break-even of lenders. E t [(1 ν(ξ i ))X t e r(τ t) + ν(ξ i ) min{m t X t + X τ, X t e r(τ t) }] = X t }{{}}{{} No Default Default m t increases in σ and ξ i. Price is set by a Nash bargaining. Consider investors having full bargaining power for simplicity. Short-Term Risk Premia = Fundamental - Price. Wenhao Short-Term Risk Premia November 22, / 26

13 Risk Premia and Return Volatility Proposition 1 (Risk Premia) The short-term risk premia, measured by the reversal in returns X t P t, increases with leverage distribution w.r.t first order stochastic dominance, and increases in idiosyncratic risks σ 2. Proposition 2 (Return Volatility) Equilibrium return volatility, measured by the quadratic variation of return paths, increases with leverage distribution w.r.t first order stochastic dominance. Wenhao Short-Term Risk Premia November 22, / 26

14 Leverage Distribution and Trading Proposition 3 (Leverage Distribution and Trading) (1) There exists a unique threshold l R + such that the optimal strategy of investors is to trade with intermediaries of leverage ξ l. (2) l increases with leverage distribution w.r.t. first order stochastic dominance. Proposition 4 (Funding Capacity Limit) Assume that there is a funding capacity limit that is smaller than shock size Q for each intermediary. Then an increase in the liquidity shock Q increases the thresholds l and high leverage intermediaries get more trading in expectation. Wenhao Short-Term Risk Premia November 22, / 26

15 Data Three asset classes with most liquid assets, to set a high bar for finding intermediary capital effects. Bond: 2002 to 2015, 600 most frequently traded bonds in TRACE. Transaction level data. Equity: 1990 to 2015, S&P500 equities, from CRSP. Daily price data. Currencies: 1990 to 2015, 33 major currencies, from Bloomberg. Daily exchange rate data. We also have a smaller set of bond trading data from Fixed Income Security Database (FISD), where dealer identities are revealed. From 1994 to Trading of insurance companies. This dataset is used to test intermediary risk sharing: asset-specific intermediary leverage v.s. aggregate leverage. Intermediary balance sheet: From merged CRSP-Compustat in WRDS. Wenhao Short-Term Risk Premia November 22, / 26

16 Key definitions Idiosyncratic risks. We regress asset returns on liquid and traded assets F t over three-month rolling windows. R i,t = α i,t + β i,t F t + ε i,t We define the idiosyncratic risk of asset i for time t to be I i,t = Var(ε i,t ), which only uses past information. Aggregate intermediary leverage. Daily variant of leverage definition in [He et al., 2016] over primary dealers. L t = sum( Market Equity + Book Debt ) / sum(market Equity) Individual leverage. Leverage = (Market Equity + Book Debt) / Market Equity Wenhao Short-Term Risk Premia November 22, / 26

17 Key definitions We measure the short-term risk premia as the subsequent return after an initial price shock, where the shock is defined as return below 2 times idiosyncratic volatility I i,t. 5 days horizon for reversal, following [Collin-Dufresne and Daniel, 2014] Exchange Rate (Against USD) Ini$al Price Shock Short-run Risk Premium > 0 Full Price Reversal AUD (5/3/2000) Date Rela$ve to Price Shock Wenhao Short-Term Risk Premia November 22, / 26

18 Summary of Data Wenhao Short-Term Risk Premia November 22, / 26

19 Risk Premia, Leverage and Idiosyncratic Risks Short-term risk premia are strongly correlated with leverage and idiosyncratic risks Risk Premia Idiosyncratic Risks Intermediary Leverage Figure: Idiosyncratic Risk Premia of Equities Wenhao Short-Term Risk Premia November 22, / 26

20 Regressions of Short-Term Risk Premia (Prop 1) Wenhao Short-Term Risk Premia November 22, / 26

21 Regressions of Short-Term Risk Premia (Prop 1) Wenhao Short-Term Risk Premia November 22, / 26

22 Leverage and Return Volatility (Prop 2) Wenhao Short-Term Risk Premia November 22, / 26

23 Leverage and Trading (Prop 3) Wenhao Short-Term Risk Premia November 22, / 26

24 Leverage and Trading (Prop 3) Wenhao Short-Term Risk Premia November 22, / 26

25 Change in Liquidity Shock and Intermediation (Prop 4) Wenhao Short-Term Risk Premia November 22, / 26

26 Conclusion We build a theory that prices idiosyncratic risks by search-and-funding mechanism with the following predictions. Short-term risk premia increases with both leverage and idiosyncratic risks. Return volatility increases endogenously with leverage. Increase in leverage reduces trading. Larger aggregate shocks flow to high-leverage intermediaries. We test these predictions with data of bonds, equities and currencies, and a subset of bond trading with dealer identities. Takeaway: Intermediaries price order imbalances (liquidity shocks) by asset idiosyncratic risks and intermediary market leverage. Wenhao Short-Term Risk Premia November 22, / 26

27 Collin-Dufresne, P. and Daniel, K. (2014). Liquidity and return reversals. He, Z., Kelly, B., and Manela, A. (2016). Intermediary asset pricing: New evidence from many asset classes. Wenhao Short-Term Risk Premia November 22, / 0