understanding dynamic mean variance asset allocation abstract we provide a new portfolio decomposition formula that sheds light on the economics of portfolio choice for investors following the mean variance mv criterion we show that the number of components of a dynamic portfolio strategy can be reduced to two the first is preference free and hedges the risk of a discount bond maturing at the investor s horizon while the second hedges the time variation in pseudo relative risk tolerance both components entail strong horizon effects in the dynamic asset allocation as a result of time varying risk tolerance and investment opportunity sets we also provide closed form solutions for the optimal portfolio strategy in the presence of market return predictability the model parameters are estimated over the period 1963 to 2012 for the u s market we show that i intertemporal hedging can be very large ii the mv criterion hugely understates the true extent of risk aversion for high values of the risk aversion parameter and the more so the shorter the investment horizon and iii the efficient frontiers seem problematic for investment horizons shorter than one year but satisfactory for large horizons overall adopting the mv model leads to acceptable results for medium and long term investors endowed with medium or high risk tolerance but to very problematic ones otherwise

optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

an asset allocation puzzle comment should the proportion of risky assets in the risky part of an investor s portfolio depend on the investor s risk aversion according to basic financial theory in particular the mutual fund separation theorem with a riskless asset the answer is no the theorem states that rational investors should divide their assets between a riskless asset and a risky mutual fund the composition of which is the same for all investors risk aversion affects only the allocation between the riskless asset and the fund however niko canner et al 1997 cmw hereafter observed that popular investment advice does not conform to this theory they reported the stocks bonds and cash allocations recommended by four advisors for conservative moderate and aggressive investors as shown in table 1 which is reproduced from cmw the advisors recommend a bond stock ratio that varies directly with risk aversion for example fidelity recommends a bond stock ratio of 1 50 for a conservative more riskaverse investor a ratio of 1 00 for a moderate less risk averse investor and a ratio of 0 46 for an aggressive still less risk averse investor the inconsistency between such advice and the separation theorem is called an asset allocation puzzle by cmw they attempted to solve the puzzle by relaxing key assumptions in the theory but finally reached a negative conclusion although we cannot rule out the possibility that popular advice is consistent with some model of rational behavior we have so far been unable to find such a model p 181 however they suggested that consideration of intertemporal trading might help resolve the puzzle in the present paper we provide theoretical support for the popular advice the two key insights are that the investor s horizon may exceed the maturity of the cash asset and that the investor rebalances the portfolio as time passes if the investor s horizon exceeds the maturity of cash which might be a money market security with maturity of one to six months then cash is not the riskless asset as is commonly assumed in the basic theory in a theory allowing portfolio rebalancing as opposed to a buy and hold framework it is not unreasonable to assume that the investor can synthesize a riskless asset a zero coupon bond maturing at the horizon using a bond fund and cash then bonds will be both in the synthetic riskless asset and in the risky mutual fund and we show that in this case the theoretical bond stock ratio varies directly with risk aversion for any hyperbolic absolute risk aversion hara investor as an example of the type of results that a specific model can produce we provide a continuous time model with closed form solutions which produces theoretical bond stock ratios similar to the popular advice the present paper is organized as follows in the next section we analyze the popular advice in terms of the theory of mutual fund separation of david cass and joseph e stiglitz 1970 we show that this theory is relevant both in static and dynamic frameworks and use it to analyze the popular advice in complete and incomplete markets in section ii we analyze the popular advice in the context of robert c merton s 1971 continuous time statement of mutualfund separation and present an illustrative model in which a crra investor makes continuous time portfolio decisions under interest rate and stock price uncertainty in section iii numerical results are compared with the popular advice section iv is a conclusion bajeux besnainou department of finance school of business and public management george washington university 2023 g street nw washington dc 20052 jordan national economic research associates 1255 23rd street nw washington dc 20037 portait cnam and essec finance chair cnam 2 rue conte paris france this research was supported by a grant from the institute for quantitative investment research we thank two anonymous referees for their comments 1 hara functions include quadratic utility which is one way of justifying mean variance preferences and constant relative risk aversion crra utility both quadratic and crra utility were considered in the cmw analysis

simultaneously learning and optimizing using controlled variance pricing price experimentation is an important tool for firms to find the optimal selling price of their products it should be conducted properly since experimenting with selling prices can be costly a firm therefore needs to find a pricing policy that optimally balances between learning the optimal price and gaining revenue in this paper we propose such a pricing policy called controlled variance pricing cvp the key idea of the policy is to enhance the certainty equivalent pricing policy with a taboo interval around the average of previously chosen prices the width of the taboo interval shrinks at an appropriate rate as the amount of data gathered gets large this guarantees sufficient price dispersion for a large class of demand models we show that this procedure is strongly consistent which means that eventually the value of the optimal price will be learned and derive upper bounds on the regret which is the expected amount of money lost due to not using the optimal price numerical tests indicate that cvp performs well on different demand models and time scales this paper was accepted by assaf zeevi stochastic models and simulation

optimal portfolio management with american capital guarantee abstract the aim of the paper is to investigate finite horizon portfolio strategies which maximize a utility criterion when a constraint is imposed on a terminal date european guarantee or on every intermediate date american guarantee we prove the optimality of the option based portfolio insurance method for both european and american cases when an expected crra utility function is maximized the american obpi is fully described in a black scholes environment as well as in the more general case of complete markets using the gittins index techniques developed by el karoui and karatzas 1995 optimality results are extended to general utility functions

pricing stock and bond options when the default free rate is stochastic we derive formulas for the valuation of call options on stocks and bonds when the defaultfree rate is stochastic the formulas highlight the role of the correlation between the unanticipated returns on the underlying security and the changes in the short term rate in determining the options value our numerical analysis indicates that option prices predicted by the proposed formula differ from those predicted by the black and scholes formula when this correlation is relatively large and the short term rate s instantaneous variance is relatively large as well moreover the proposed formula predicts higher lower stock option prices than those predicted by the black and scholes formula for correlation values that are lower higher than some positive critical value

on the minimax complexity of pricing in a changing environment we consider a pricing problem in an environment where the customers willingness to pay wtp distribution may change at some point over the selling horizon customers arrive sequentially and make purchase decisions based on a quoted price and their private reservation price the seller knows the wtp distribution pre and postchange but does not know the time at which this change occurs the performance of a pricing policy is measured in terms of regret the loss in revenues relative to an oracle that knows the time of change prior to the start of the selling season we derive lower bounds on the worst case regret and develop pricing strategies that achieve the order of these bounds thus establishing the complexity of the pricing problem our results shed light on the role of price experimentation and its necessity for optimal detection of changes in market response wtp our formulation allows for essentially arbitrary consumer wtp distributions and purchase request patterns

the numeraire portfolio abstract a portfolio formed from a given list of assets is defined as a numeraire portfolio for the list if a it is self financing b its value is always positive and c zero is always the best conditional forecast of the numeraire dominated rate of return of every asset on the list the numeraire portfolio exists if and only if there are no profit opportunities from trading assets on the list for a sample list of heterogeneous assets nyse size quintile portfolios corporate bonds and short term bills numeraire dominated returns are similar to market model forecast errors and as abnormal return measures clearly dominate market adjusted returns

optimal consumption and portfolio policies when asset prices follow a diffusion process abstract we consider a consumption portfolio problem in continuous time under uncertainty a martingale technique is employed to characterize optimal consumption portfolio policies when there exist nonnegativity constraints on consumption and on final wealth we also provide a way to compute and verify optimal policies our verification theorem for optimal policies involves a linear partial differential equation unlike the nonlinear partial differential equation of dynamic programming the relationship between our approach and dynamic programming is discussed we demonstrate our technique by explicitly computing optimal policies in a series of examples in particular we solve the optimal consumption portfolio problem for hyperbolic absolute risk aversion utility functions when the asset prices follow a geometric brownian motion the optimal policies in this case are no longer linear when nonnegativity constraints on consumption and on final wealth are included by these examples one can see that our approach is much easier than the dynamic programming approach

bayesian dynamic pricing policies learning and earning under a binary prior distribution motivated by applications in financial services we consider a seller who offers prices sequentially to a stream of potential customers observing either success or failure in each sales attempt the parameters of the underlying demand model are initially unknown so each price decision involves a trade off between learning and earning attention is restricted to the simplest kind of model uncertainty where one of two demand models is known to apply and we focus initially on performance of the myopic bayesian policy mbp variants of which are commonly used in practice because learning is passive under the mbp that is learning only takes place as a by product of actions that have a different purpose it can lead to incomplete learning and poor profit performance however under one additional assumption a constrained variant of the myopic policy is shown to have the following strong theoretical virtue the expected performance gap relative to a clairvoyant who knows the underlying demand model is bounded by a constant as the number of sales attempts becomes large this paper was accepted by gerard p cachon stochastic models and simulation

implications of the sharpe ratio as a performance measure in multi period settings we study efiects of using sharpe ratio as a performance measure for compensating money managers in a dynamic and frictionless market setting first we demonstrate that with such a performance measure the manager s focus on the short horizon performance is detrimental to the investor s long horizon performance numerical experiments illustrate that when returns are iid the performance loss is signiflcant even when the investor s investment horizon is not much longer than the manager s when expected returns are mean reverting the performance loss is exacerbated second we show that sharpe ratio maximization strategies tend to increase decrease the risk in the later part of the optimization period after a bad good performance in the earlier part of the optimization period as illustrated by a simulation exercise this prediction is in agreement with empirical observations and it presents a rational expectations alternative to the prevalent tournament theory explanation

voting and imitative behavior political behavior generates private benefits by helping people fit in with desired friends a voter imitates other voters but at the same time they imitate him an equilibrium solution requires exogenous variables the narrow self interest of the participants the reduced form makes one s vote a function of the narrow self interest of others as well as one s own in accord with the model a person s party identification depends on his ethnic group s current income and its income in 1909 as well as his own income i introduction what determines how people vote most economists such as peltzman 1980 have emphasized self interested motivations but kau and rubin 1982 and kalt and zupan 1984 claim that ideology based in part on altruism influences voting patterns both hypotheses have the same fundamental flaw they focus on the consequences of the policies for which people vote in the peltzman model a person votes for those policies which maximize his real income i call this narrow self interest in the standard altruism models of economists a person maximizes some weighted average of the real income of himself and others 1 however an individual s vote has a minuscule impact on the outcome of any election therefore his vote for a policy yields extremely small expected returns through the impact of that policy on the voter other returns from voting will dominate in determining behavior if such returns exist some economists for example brennan and buchanan 1984 have recognized this problem with the standard or economic view no one however has developed an alternative theory based on other returns to voting the key point of this paper is that political behavior can generate private benefits by helping people fit in with desired friends and associates a herd effect to give this phenomenon a name political positions are thus chosen not because they produce the desired outcomes for voters but rather because voters want to associate with certain people who have certain positions that is people imitate others in choosing political positions the idea for imitation in political positions is hardly new berelson et al 1954 provide a prima facie case for imitation in voting behavior they found that a person s political position was closely related to the political positions of his coworkers and friends of course these results could be attributable to the fact that these groups share common characteristics but the berelson data also show that people change their political position toward that of their associates a phenomenon more difficult to explain by the common characteristic hypothesis imitation is uninteresting as a predictor of behavior by itself however a voter imitates other voters but at the same time they imitate him an equilibrium solution requires exogenous variables i assume these to be the narrow self interest of the participants the resulting model differs from a simple narrow self interest model in the reduced form one s political decision is a function of the narrow self interest of others as well as one s own narrow self interest imitation along with the self interest of the participants leads both to additional tests of imitation and makes the imitation model of interest in understanding political behavior imitation could be an attempt to please others who have a primitive preference for friends who imitate themselves alternatively imitation could signal an offer of friendship by the imitator without invoking preferences for friends who imitate such signalling could therefore explain why people care whether somebody imitates their political behavior or not imitation could also arise from another process people s views of appropriate behavior could be determined by the behavior of those with whom they associate 2 narrow self interest can also generate a form of imitation imitating the behavior of people with like interests who are more informed

dynamic asset allocation with mean variance preferences and a solvency constraint abstract the aim of this article is to analyze the portfolio strategies that are mean variance efficient when continuous rebalancing is allowed and a solvency constraint wealth positiveness is imposed at each point in time under very general assumptions ito processes for the security price dynamics those efficient strategies are identified as synthetic put options on the particular inefficient portfolio yielding the return with minimal second moment this general characterization allows us to derive a closed form formula for the optimal portfolio weights when the investment opportunity set is constant the optimal weights are explicit functions of the current market index the formula is then used to simulate dynamically efficient strategies for different horizons and targets and to describe the time pattern of the allocation to stocks versus bonds

dynamic asset allocation in a mean variance framework the aim of this article is to analyze the portfolio strategies that are mean variance efficient when continuous rebalancing is allowed between the current date 0 and the horizon t under very general assumptions when a zero coupon bond of maturity t exists the dynamic efficient frontier is a straight line the slope of which is explicitly characterized every dynamic mean variance efficient strategy can be viewed as buy and hold combinations of two funds the zero coupon bond of maturity t and a continuously rebalanced portfolio an appropriate dynamic strategy defining the latter is explicitly derived for two particular price processes and comparisons of the efficient frontiers static versus dynamic are provided in these cases

on dynamic decision making to meet consumption targets we investigate a dynamic decision model that facilitates a target oriented decision maker in regulating her risky consumption based on her desired target consumption level in every period in a finite planning horizon we focus on dynamic operational decision problems of a firm where risky cash flows are being resolved over time the firm can finance consumption by borrowing or saving to attain prescribed consumption targets over time to evaluate the ability of the consumption in meeting respective targets we propose the consumption shortfall risk csr criterion which has salient properties of attainment content starvation aversion subadditivity and positive homogeneity we show that if borrowing and saving are unrestricted and their interest rates are common the optimal policy that minimizes the csr criterion is to finance consumption at the target level for all periods except the last for general convex dynamic decision problems the optimal policies correspond to those that maximize an additive

dynamic pricing under a general parametric choice model we consider a stylized dynamic pricing model in which a monopolist prices a product to a sequence of t customers who independently make purchasing decisions based on the price offered according to a general parametric choice model the parameters of the model are unknown to the seller whose objective is to determine a pricing policy that minimizes the regret which is the expected difference between the seller s revenue and the revenue of a clairvoyant seller who knows the values of the parameters in advance and always offers the revenue maximizing price we show that the regret of the optimal pricing policy in this model is theta sqrt t by establishing an omega sqrt t lower bound on the worst case regret under an arbitrary policy and presenting a pricing policy based on maximum likelihood estimation whose regret is cal o sqrt t across all problem instances furthermore we show that when the demand curves satisfy a well separated condition the t period regret of the optimal policy is log t numerical experiments show that our policies perform well

dynamic asset allocation for stocks bonds and cash closed form solutions for hara optimal portfolios are obtained in a dynamic portfolio optimization model in three assets stocks bonds and cash in a vasicek type model of stochastic interest rates with correlated stock prices the hara is a buy and hold combination of a zero coupon bond with maturity matching the investor s horizon and a crra mutual fund this simple characterization facilitates insights about investor behavior over time and provides explanations on the rational use of convex versus concave investment strategies the model illuminates clearly the role of the different market parameters and relative risk aversion in portfolio strategies

an exact bond option formula this paper derives a closed form solution for european options on pure discount bonds assuming a mean reverting gaussian interest rate model as in vasicek 8 the formula is extended to european options on discount bond portfolios

a minimum variance result in continuous trading portfolio optimization the problem of minimizing the variance of discounted wealth at the end of a fixed period is solved when the expectation of terminal wealth is constrained to a specified investment goal the results are obtained in a continuous trading framework under the assumption that the funds can be exchanged between a riskless bond and a stock whose discounted price is described by a geometric brownian motion transaction costs are ignored i e the market is frictionless and unlimited borrowing is permitted at the same rate as the return on the bond typically the optimal trading policy under the above assumptions involves a highly leveraged investment in the stock in the early stages followed by an accumulation of the bond in the later stages numerical results are provided as an illustration of the theory

semi analytical solutions for dynamic portfolio choice in jump diffusion models and the optimal bond stock mix this paper studies the optimal portfolio selection problem in jump diffusion models where an investor has a hara utility function and there are potentially a large number of assets and state variables more specifically we incorporate jumps into both stock returns and state variables and then derive semi analytical solutions for the optimal portfolio policy up to solving a set of ordinary differential equations to greatly facilitate economic insights and empirical applications of jump diffusion models to examine the effect of jump risk on investors behavior we apply our results to the bond stock mix problem and particularly revisit the bond stock ratio puzzle in jump diffusion models our results cast new light on this puzzle that unlike pure diffusion models it cannot be rationalized by the hedging demand assumption due to the presence of jumps in stock returns

pricing interest rate derivative securities this article shows that the one state variableinterest rate models of vasicek 1977 and cox ingersoll and ross 1985b can be extended sothat they are consistent with both the current termstructure of interest rates and either the currentvolatilities of all spot interest rates or the currentvolatilities of all forward interest rates theextended vasicek model is shown to be very tracta ble analytically the article compares option pricesobtained using the extended vasicek model withthose obtained using a number of other models