Asset Prices and Institutional Investors: Discussion Suleyman Basak and Anna Pavlova Ralph S.J. Koijen University of Chicago and NBER June 2011 Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 1 / 21
Delegation and Asset Pricing Lot of asset pricing theory abstracts from delegation and decentralization Quite remarkable given how important agency theory is in …nance and economics more broadly This paper argues that we may need to understand the interaction between delegation and asset pricing I I agree Important and transparent paper, with hopefully many followers Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 2 / 21
Size of the Mutual Fund Industry For instance, consider the size of the mutual fund industry relative to total market cap 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1985 1990 1995 2000 2005 2010 Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 3 / 21
Model: Endowments and Preferences Two agents endowed with initial wealth shares λ and 1 � λ Agents di¤er in terms of their preferences/objective function I Retail investors: u R ( W T ) = log W T I Institutional investors ( a , b > 0): u I ( W T , I T ) = ( a + bI T ) log W T These preferences imply: ∂ u I ( W T , I T ) / ∂ W T = a + bI T , W T and hence increasing in the benchmark, I T Same in other models of preferences, for instance: 1 1 � γ ( W T / I T ) 1 � γ , u I ( W T , I T ) = just a lot more tractable in GE! Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 4 / 21
Model: Technology N assets of which M are included in the benchmark Log-normal dividends: h i d D jt = D jt µ j d t + σ j d ω t , where the last asset of the market and the index are residuals The market and index have geometric dividends too: d I t = I t [ µ I d t + σ I d ω t ] , d D MKT , t = D MKT , t [ µ MKT d t + σ MKT d ω t ] Useful trick to make the problem tractable Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 5 / 21
Main Insights and Mechanism For stocks in the index: 1 I Stock values are higher I Volatility higher and counter-cyclical I Sharpe ratios lower and counter-cyclical I Stocks tend to comove "excessively" and correlation varies over time No e¤ect for non-index stocks 2 Credit markets play an important role 3 = ) Restricticting leverage may lower index values Main mechanism: Wealth shocks determine the relative weight on the two agents’ objective functions Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 6 / 21
Discussion Wealth e¤ects play central role: What drives wealth e¤ects? 1 How does delegation a¤ect asset pricing? 2 Frequency 1 Performance measurement 2 All comments should be interpreted as a wish list – paper is great as it is! Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 7 / 21
Discussion: Wealth distribution In two-agent models, the wealth distribution among agents plays an important role In this case, we are interested in I t / S t , where I t is the size of the fund industry and S t is the size of the equity market I Note: Size MF industry as a proxy for institutional investors Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 8 / 21
Discussion: Wealth distribution To understand empirical determinants, it may be useful to start from two budget constraints: Size market: 1 S t + 1 = S t R S t + 1 + E t + 1 , where R S t is the market return and E t net issuances minus cash dividends Size mutual fund industry: 2 I t + 1 = I t R I t + 1 + F t + 1 where R I t is the fund industry return and F t the net ‡ow Follows long tradition in …nance and macro I Campbell and Shiller (1988), Lettau and Ludvigson (2001), Gourinchas and Rey (2007), Corsetti and Konstantinou (2011) Natural application to mutual fund industry Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 9 / 21
A Valuation Equation We are interested in an expression of m t � v t Write: � � 1 + E t V t + 1 = ( V t + E t ) R S R S t + 1 = V t t + 1 , V t where V t = S t � E t In logs: � � 1 + E t + r S v t + 1 = v t + ln t + 1 V t We do the same for the mutual fund industry � � 1 + F t + r I m t + 1 = m t + ln t + 1 , M t where M t = I t � F t Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 10 / 21
A Valuation Equation It then follows: ( m t + 1 � v t + 1 ) � ( m t � v t ) = � � � � � � 1 + F t 1 + E t r I t + 1 � r S + ln � ln , t + 1 M t V t or: ( m 2010 � v 2010 ) � ( m 1980 � v 1980 ) = � � � � � � 2010 2009 2009 1 + F j 1 + E j ∑ r I j � r S ∑ ∑ + ln � ln j M j V j j = 1981 j = 1980 j = 1980 | {z } | {z } | {z } Valuation e¤ect Flow e¤ect Financing e¤ect Hence, we can measure the importance of the wealth e¤ect coming from three channels! Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 11 / 21
Implication of the Valuation Equation By taking conditional expectations, we m t � v t has to predict either relative returns, future ‡ows or net issuances: � � ∞ r I t + s � r S ∑ m t � v t � lim s ! ∞ E t ( m s � v s ) = � E t t + s s = 1 | {z } Valuation e¤ect � � �� ∞ 1 + F t + s ∑ � E t ln M t + s s = 0 | {z } Flow e¤ect � � �� ∞ 1 + E t + s ∑ + E t ln V t + s s = 0 | {z } Financing e¤ect Logic as in Cochrane (2008): PD has to predict returns or dividends, or both Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 12 / 21
Derivations: Valuation equation I will use the accounting equation in this discussion to interpret the history between 1980 and 2010: ( m 2010 � v 2010 ) � ( m 1980 � v 1980 ) = � � � � � � 2010 2009 2009 1 + F j 1 + E j ∑ r I j � r S ∑ ∑ + log � log j M j V j j = 1981 j = 1980 j = 1980 | {z } | {z } | {z } Valuation e¤ect Flow e¤ect Financing e¤ect This paper concentrates on the …rst component Could be that all terms co-move, which would provide a broader interpretation of the model Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 13 / 21
A Valuation Equation: Empirical Results Decomposition of changes in m t � v t in ln ( 1 + E t / V t ) , ln ( 1 + F t / M t ) , and r I t � r S t -1 0.2 m-v ln(1+E/V) 0.1 -2 0 -3 -0.1 -4 -0.2 1985 1990 1995 2000 2005 2010 1985 1990 1995 2000 2005 2010 0.2 0.05 r I -r S ln(1+F/M) 0.1 0 0 -0.1 -0.2 -0.05 1985 1990 1995 2000 2005 2010 1985 1990 1995 2000 2005 2010 Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 14 / 21
A Valuation Equation: Empirical Results Average change ("Trend") � r I � r S � I E = � 0 . 6 % I E ( F / M ) = 5 . 6 % I E ( E / V ) = � 1 . 9 % Standard deviation of changes ("Cycle") � r I � r S � I σ = 1 . 5 % I σ ( F / M ) = 6 . 5 % I σ ( E / V ) = 6 . 6 % Contemporaneous correlations below 10% = ) Caveat: For instance ‡ows from past returns, so correlations require more work to be conclusive Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 15 / 21
Discussion: Frequency Perhaps the most striking feature of the wealth distribution is the secular trend Model implies trends in volatilities, Sharpe ratios, index values for index versus non-index stocks: I Long-term decline in risk premia I Long-term increase in volatility I Di¤erential predictability I What if all was unexpected? Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 16 / 21
Discussion: Performance measurement To measure the performance of fund managers, it is common practice to regress fund returns on a benchmark: r MF = α + β R BM + ε One can imagine two benchmarks now: I Aggregate stock market I Index of the institutional investor Neither of them will give a zero alpha as: I There is a two-factor structure now I Risk prices move over time due to the share of fund managers changing = ) Benchmarks are now endogenous I’d be interested in understanding the implications for performance measurement Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 17 / 21
Summary Great paper on a topic that deserves a lot more attention Closed-form solutions very helpful and this model is a "benchmark" going forward Wealth distribution plays an important role in many of these models I use two budget constraints to quantify some of the forces that drive the wealth distribution The interaction with ‡ows and the …nancing decisions of …rms may be particularly interesting directions to extend the model Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 18 / 21
Derivations: Dynamics Aggregate Market Start from the return de…nition: t + 1 = N t P t + 1 + N t D t + 1 R S N t P t This implies: S t + 1 = S t R S t + 1 + N t + 1 P t + 1 � N t P t + 1 � N t D t + 1 This results in E t : E t + 1 = N t + 1 P t + 1 � N t P t + 1 � N t D t + 1 | {z } | {z } Net issuances Aggregate cash dividends Koijen (U. of Chicago and NBER) Asset Prices and Institutional Investors June 2011 19 / 21
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