Balance,growth and diversity of financial markets

A financial market comprising of a certain number of distinct companies is considered, and the following statement is proved: either a specific agent will surely beat the whole market unconditionally in the long run, or (and this “or” is not exclusive) all the capital of the market will accumulate in one company. Thus, absence of any “free unbounded lunches relative to the total capital” opportunities lead to the most dramatic failure of diversity in the market: one company takes over all other until the end of time. In order to prove this, we introduce the notion of perfectly balanced markets, which is an equilibrium state in which the relative capitalization of each company is a martingale under the physical probability. Then, the weaker notion of balanced markets is discussed where the martingale property of the relative capitalizations holds only approximately, we show how these concepts relate to growth-optimality and efficiency of the market, as well as how we can infer a shadow interest rate that is implied in the economy in the absence of a bank.      

Local time and the pricing of time-dependent barrier options

A time-dependent double-barrier option is a derivative security that delivers the terminal value φ(S _T ) at expiry T if neither of the continuous time-dependent barriers b _±:[0,T]→ℝ₊ have been hit during the time interval [0,T]. Using a probabilistic approach, we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions φ, barrier functions b _± and linear diffusions (S _t ) _t∈[0,T]. We show that the barrier premium can be expressed as a sum of integrals along the barriers b _± of the option’s deltas Δ _±:[0,T]→ℝ at the barriers and that the pair of functions (Δ ₊,Δ ₋) solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.     

A Quarterly Transactions-based Index of Institutional Real Estate Investment Performance and Movements in Supply and Demand

This article presents a methodology for producing a quarterly transactions-based index (TBI) of property-level investment performance for U.S. institutional real estate. Indices are presented for investment periodic total returns and capital appreciation (or price-changes) for the major property types included in the NCREIF Property Index. These indices are based on transaction prices to avoid appraisal-based sources of index “smoothing” and lagging bias. In addition to producing variable-liquidity indices, this approach employs the Fisher-Gatzlaff-Geltner-Haurin (Real Estate Econ., 31: 269–303, 2003) methodology to produce separate indices tracking movements on the demand and supply sides of the investment market, including a “constant-liquidity” (demand side) index. Extensions of Bayesian noise filtering techniques developed by Gatzlaff and Geltner (Real Estate Finance, 15: 7–22, 1998) and Geltner and Goetzmann (J. Real Estate Finance Econ., 21: 5–21, 2000) are employed to allow development of quarterly frequency, market segment specific indices. The hedonic price model used in the indices is based on an extension of the Clapp and Giacotto (J. Am. Stat. Assoc., 87: 300–306, 1992) “assessed value method,” using a NCREIF-reported recent appraised value of each transacting property as the composite “hedonic” variable, thus allowing time-dummy coefficients to represent the difference each period between the (lagged) appraisals and the transaction prices. The index could also be used to produce a mass appraisal of the NCREIF property database each quarter, a byproduct of which would be the ability to provide transactions price based “automated valuation model” estimates of property value for each NCREIF property each quarter. Detailed results are available at .     

Weighted V@R and its Properties

The paper deals with the study of a coherent risk measure, which we call Weighted V@R. It is a risk measure of the form where μ is a probability measure on [0,1] and TV@R stands for Tail V@R. After investigating some basic properties of this risk measure, we apply the obtained results to the financial problems of pricing, optimization, and capital allocation. It turns out that, under some regularity conditions on μ, Weighted V@R possesses some nice properties that are not shared by Tail V@R. To put it briefly, Weighted V@R is “smoother” than Tail V@R. This allows one to say that Weighted V@R is one of the most important classes (or maybe the most important class) of coherent risk measures.     

Bank Competition and Financial Stability

Under the traditional “competition-fragility” view, more bank competition erodes market power, decreases profit margins, and results in reduced franchise value that encourages bank risk taking. Under the alternative “competition-stability” view, more market power in the loan market may result in higher bank risk as the higher interest rates charged to loan customers make it harder to repay loans, and exacerbate moral hazard and adverse selection problems. The two strands of the literature need not necessarily yield opposing predictions regarding the effects of competition and market power on stability in banking. Even if market power in the loan market results in riskier loan portfolios, the overall risks of banks need not increase if banks protect their franchise values by increasing their equity capital or engaging in other risk-mitigating techniques. We test these theories by regressing measures of loan risk, bank risk, and bank equity capital on several measures of market power, as well as indicators of the business environment, using data for 8,235 banks in 23 developed nations. Our results suggest that—consistent with the traditional “competition-fragility” view—banks with a higher degree of market power also have less overall risk exposure. The data also provides some support for one element of the “competition-stability” view—that market power increases loan portfolio risk. We show that this risk may be offset in part by higher equity capital ratios.

Fortune Favours the Bold? Exploring Tournament Behavior among Australian Superannuation Funds

In this paper we investigate the tournament induced risk-shifting behavior of Australian “multi-sector growth funds”. We apply a regression-based methodology and examine tournaments based on the calendar year and the financial year. In our core analysis we find evidence in favor of Taylor’s (J Econ Behav Organ 1455:1–11, 2003) risk shifting tournament hypothesis for financial year-end tournaments. Apart from the standard tournament hypothesis we also report a range of findings regarding stability; fund age; and fund size. Support for the Taylor hypothesis generally continues across these variations as well.

Skewness of Returns, Capital Adequacy, and Mortgage Lending

We calibrate a simulation model of credit value-at-risk for mortgage lending to UK experience. Simulations to capture the skewness of returns that might arise in the context of a financial crisis suggest that the IRB calculations of the new Basel Accord can substantially understate prudential capital adequacy. The same model shows that raising capital requirements has only a small impact on bank funding costs. We conclude that Pillar 2 supervisory review should increase capital requirements above IRB levels for secured bank assets—those whose returns can potentially fall furthest, relative to other, normally “riskier” assets, in extreme outcomes. JEL classification: G21, G28, R31. Presented at the December 2003 conference at the University of Tor Vegata, Rome. We are grateful for comments from William Lang, Mario Onarato, Larry Wall, and from an anonymous referee. All errors and omissions are our own responsibility. “The lady doth protest too much, methinks. The Queen's response to the players in Hamlet, Act 3, scene 2.     

Risk-neutral compatibility with option prices

A common problem is to choose a “risk-neutral” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure” by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of “compatibility” between X and the prices of our options, and this poses some significant mathematical difficulties.