Econ 138 Financial and Behavioral Economics Lecture 11: Diversification and Microfinance Ulrike Malmendier UC Berkeley Th, February 28, 2008 Organization Lunches! -- Felipe and others remarked that many of you have class right after this one. Wed? (alternating) Midterm: -- Many impressive exams! -- Remember graded on a curve ... -- As long as you got Q1 AND part (a)-(g) of Q2, you are on track. -- If you were struggling with the first 16 points ... red flag! Typically, this seemed to indicate some difficulty with the basics (set up of the problem, general idea, ...). Come and talk to me! 1 Diversification We have studied how debt capacity may be limited due to Moral Hazard. Diversification: Might it help if the manager has more than one investment project? Intuition: Since manager is risk neutral, compensate only when both projects succeed. Lenders lose less money in the case of failure, and manager will want to work hard on both projects if paid enough: Rm,2 &gt; 0, Rm,1 = Rm,0 = 0. -- Formally, we show (only) that there always exists one optimal incentive scheme with Rm,2 &gt; 0, Rm,1 = Rm,0 = 0: Given the above contract, when does the manager work? -- Works hard: p2 Rm,2. H -- Shirks: p2 Rm,2 + 2B. L -- Hence, manager works hard on both projects rather than shirking (constraint 1, or `IC1') on both if and only if: p2 Rm,2 p2 Rm,2 + 2B H L 2B (pH + pL)Rm,2 p -- The manager works hard on both projects rather than shirking on one (constraint 2, or `IC2') iff pH Rm,2p B (by shirking on one project, the manager reduces the probability of full success by pH , i.e. the probability that that project succeeds, times p, i.e. the reduction in the second project's probability of success.) IC2 says: loss from shriking on 1 outweighs gain (B). -- Since pH &gt; 1 (pH + pL), the IC2 is automatically satisfied: 2 2B (pH + pL)Rm,2 p 1 (pH + pL)Rm,2p B 2 2B -- Hence the lowest Rm,2 = p(p +p ) . H L -- Makes intuitive sense: the larger the benefits of shirking or the smaller the difference in probability the larger the reward needs to be to induce hard work. Back to the big question: How does this compare to the baseline case? Can we finance the projects more often or less often? 2B We derived Rm,2 = p(p +p ) , and hence the expected payoff of the H L 2B manager (if working hard) is p2 Rm,2 = p2 p(p +p ) . H H H L To simplify the notation, denote d = p pL , i.e., 1 - d = p pH . Hence, L +pH L +pH B the expected payoff of the manager is 2pH (1 - d) p . B Thus, both projects are funded if: 2pH (R - (1 - d) p ) 2I - 2C. The right hand side is what investors are putting up, while the left hand side is the total expected return when the manager works hard, minus the expected payment to the manager. B Simplifies to pH [R - (1 - d) p ] I - C. Compare to the base case: -- Everything is the same except for the (1 - d) term. -- More projects are undertaken because of the ability to pledge income from one project to pay the debts on another. Intuition: Income from one project can be used to relax limited liability constraint in case of failure of the other project! Intuition 2: Diversification helps remedy the incentive problem (as if private benefit reduced from B to (1 - d)B) similar to how more cash helps: there is more at stake for the manager if he shirks / the investor gets less of the return in the good state and hence the manager gets more. -- If investors can choose to finance 0, 1, or 2 projects, how many will they finance? NOTE: very different notion of the benefits of diversification!! -- `Newspaper notion' and `asset pricing notion': we limit the risk of a bad outcome, given investors' risk aversion. -- `Moral Hazard notion': cross-pledging = borrower pledges her payoff on one project as &quot;collateral&quot; for another project. -- d is an agency-based measure of economies of diversification. This result generalizes &quot;easily&quot; to multiple independent projects. (The math is a bit tedious.) -- As the number of independent projects approaches infinity, the financing condition converges to pH R - B I - C. -- So the agency problem is almost eliminated: simply pay the manager an (expected) amount per project equal to her private benefit from shirking (her cost to working), and she will work hard on all the projects. -- This would get almost every NPV project financed. Those that aren't financed have NPV less than B. Similar results hold in the case where we have variable investment size projects. BUT: results rest heavily on the projects being independent. -- If the projects are partially correlated, the incentive problems are worse. -- If they are perfectly correlated there is no benefit at all. Intuition: the two projects are really just one larger project. Some problems with diversification in the real world: -- Impossible to find completely independent projects; almost certainly some correlation simply by virtue of being part of same firm. -- Even finding mostly uncorrelated projects may be impossible without going outside the firm's area of expertise. (&quot;Diversification discount&quot; literature!) -- A larger firm may require more upkeep costs, or the managers may not be able to effectively run multiple independent projects.(Another potential reason for &quot;diversification discount&quot;) Key Points: -- Having diverse projects reduces the impact of the manager's agency problems. -- But correlation between the projects reduces this impact, and firms may be limited in the number of uncorrelated projects they have available. -- So in practice the agency problem is never eliminated. Costs of Collateralization Diversification helps increase financing / remedy incentive problem since one project is used as a kind of `collateral' for the other project. More generally: not only cash but any type of collateral can help to relax financing constraints and help company secure a loan. BUT: pledging collateral can be inefficient / cause a deadweight loss. Reasons: 1. There may be transaction costs associated with collecting the assets. For example legal fees, uncertainty about the <a href="/keyword/judicial-process/" >judicial process</a> . 2. The firm may value the asset more highly than the lender, e.g., because the equipment requires training to use or there are synergies with other assets the firm holds. 3. Some assets are hard to sell. -- Example: Trade secrets that are legally unprotected = hard to sell because buyer needs to know just enough to know the process is useful, but not enough that they can simply use the idea without paying. 4. Firm may be risk averse = pledging to give all assets may be too much to give up. Particularly a problem if manager is concerned about her job security. 5. `Classic Moral Hazard': Firm may not take good enough care of assets if they are pledged since the maintenance problems may not matter to them. 6. Some assets may be worthless without a manager attached = the lender would have to hire a manager to run the asset and pay that manager a moral hazard premium lessening the value of the asset to the lender. 2 Microfinance Lending to the very poor not a new idea, but previously proved a failure with high default rates and corruption large problems. Microfinance backers claim it is a &quot;win-win&quot; situation helping borrowers while earning profits for lenders. Although evidence is mixed on the profitability of loaning to the poorest, microfinance is a clear improvement on earlier lending programs. What are they doing differently than previous lenders? Basic Facts: -- Loans have repayment rates of over 90% compared to previous government subsidized loans with rates of 50-70% or even lower. -- Institutions differ in their borrower characteristics. For some, average loans are tiny ($100 or less for some), while others serve the somewhat wealthier poor and have larger loans. -- Most loans short term, usually from months to a year. -- Most have mostly female borrowers, often over 90%. -- Most do not require collateral. -- Many use group lending. -- Most server rural customers, but some serve urban areas. -- All offer chances for repeated lending and larger loans to borrowers who repay. -- Some institutions are sustainable (without any outside subsidies), but not those that serve the poorest. Note on the last point: This is a large point of debate. Some advocate using only self-sustainable microfinance, others argue that increasing interest rates will discourage too many borrowers. Depends on elasticity of borrower demand and the value lost by the discouraged borrowers. Explanations for the success of microfinance: -- Two explanations relate to what we covered / discussed previously in class: 1. Peer monitoring and 2. Collateral, though `social collateral.' -- Other explanations: 1. Progressive lending More below. 2. Weekly repayment schedules Often begin before project could produce much benefit, so partially paid for out of consumption stream. Borrowers left with lower balances after investment pays off so less incentive to not repay. Disciplines borrowers cash management. 3. Forced savings. Many banks force buyers to invest a certain amount monthly. Such accounts act as collateral that the bank can seize in the event of default. &quot;Progressive Lending&quot;: Refers to fact that successful repayment of one loan leads to preferential treatment for future loans while default will lead to no future loans. If borrower values the future enough, will not want to risk default on loans now. Model: expand our previous model to a repeated game. Key (additional) assumptions for this model: No certain ending to the lending relationship (unless borrower defaults). Less important assumption: Borrower has no outside financing options (similar conclusions hold if this is relaxed). -- Assume C = 0 for simplicity -- Investment can not be financed in the one shot version of the game (C &lt; C) -- Financing is not profitable if the manager will shirk. We begin with the basic fixed investment moral hazard model. We then turn this model into a repeated game. (We will go over some basics of game theory, but nothing too complicated.) Informal Definition: A game is a situation where two or more players make strategic decisions and the utility of the players is determined by some known rule (possibly involving random factors). Players wish to maximize their utility by making good choices. -- In fact, our model already was a game! We just never thought of it that way. Two primary concepts to predict how people will play the game: -- Backwards induction: when people make a decision now, they should correctly predict how people will make decisions the rest of the game and account for it in their current decision. -- Nash Equilibrium: everyone should be playing the best they can given the play of everyone else. Much debate about the empirical validity of these concepts as predictors of play, but their simplicity (and the lack of a better solution concept) leads to their almost uniform use. (If you don't remember those concepts, remind yourself from your 101A or similar notes.) A repeated game is an extension of this. -- Players repeat a game an infinite number of times. -- Each game is worth as much as the game preceding it, so the player P t evaluates their utility as t=0 Ut where Ut is the utility the player earns at time t. -- Since there's nothing infinite in the real world, an infinite game can be thought of as a game repeated an unknown number of times where the probability of the game ending after any period is 1 - . In our case, this will be fairly simple as each player has only one decision per game (lend or not lend, work hard or shirk). We will ignore certain complex strategies (for simplicity purposes and to avoid discussion of multiple possible equilibrium strategies): -- We will constrain the lender to either never lend or lend every time until the project fails and then never lend again. (Hard Exercise: Examine what happens if you relax this assumption and allow the lender to withhold financing for only a limited period of time.) -- Can show that borrower works hard every time if she works hard the first time (and never works hard if she doesn't work hard the first time). Pt= t t+1 t=0 pH Rm So, borrower's expected utility from working hard is: Expected utility from shirking is: Pt= (B + pLRm) tpt . t=0 L t= tpt+1R So we need that: m &gt; t=0 H buyer is to work hard. P Pt= t t t=0 (B + pLRm) pL if the -- On the LHS, factor out pH and use the formula for a geometric series pH R to get 1-p m . H -- On the RHS simply use the geometric series formula to get B+pLRm 1-pL -- Now multiply by 1 - pL and rearrange to get 1 - pL - 1) B pH Rm - pLRm + pH Rm( 1 - pH Compare to before: Borrower worked hard only if (p)Rm B. Easier to satisfy-LHS is larger than base case while RHS is the same. -- We ignore the analysis of the lender here-if pledgable income is larger than I they will invest until the project fails, otherwise they will never invest. So financing occurs more often when the interaction is repeated because the value of future lending helps increase the expected cost of current misbehavior by the manager. -- Similar to logic of diversification (multiple projects)! Indeed, may understate case if future loans are larger and more valuable.