Department of Economicshttps://commons.lib.niu.edu/handle/10843/132782020-06-06T02:01:10Z2020-06-06T02:01:10ZNash Bargaining Over Margin Loans to Kelly GamblersGarivaltis, Alexhttps://commons.lib.niu.edu/handle/10843/203022019-09-03T16:06:47Z2019-01-01T00:00:00ZNash Bargaining Over Margin Loans to Kelly Gamblers
Garivaltis, Alex
I derive practical formulas for optimal arrangements between sophisticated stock market investors (namely, continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e. the market portfolio). Rather than, say, the broker posting a monopoly price for margin loans, the gambler agrees to use a greater quantity of margin debt than he otherwise would in exchange for an interest rate that is lower than the broker would otherwise post. The gambler thereby attains a higher asymptotic capital growth rate and the broker enjoys a greater rate of intermediation profit than would obtain under non-cooperation. If the threat point represents a vicious breakdown of negotiations (resulting in zero margin loans), then we get an elegant rule of thumb: the negotiated interest rate is (3/4)r +(1/4)(ν−σ^2/2), where r is the broker’s cost of funds, ν is the compound-annual growth rate of the market index, and σ is the annual volatility. We show that, regardless of the particular threat point, the gambler will negotiate to size his bets as if he himself could borrow at the broker’s call rate.
2019-01-01T00:00:00ZCover's Rebalancing Option With Discrete Hindsight OptimizationGarivaltis, Alexhttps://commons.lib.niu.edu/handle/10843/193382019-03-28T21:21:12Z2019-03-03T00:00:00ZCover's Rebalancing Option With Discrete Hindsight Optimization
Garivaltis, Alex
We study T. Cover’s rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $1 deposit into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A rebalancing rule (or fixed-fraction betting scheme) amounts to fixing an asset allocation (i.e. 200% stocks and -100% bonds) and then continuously executing rebalancing trades to counteract allocation drift. Restricting the hindsight optimization to a small number of rebalancing rules (i.e. 2) has some advantages over the pioneering approach taken by Cover & Company in their brilliant theory of universal portfolios (1986, 1991, 1996, 1998), where one’s on-line trading performance is benchmarked relative to the final wealth of the best unlevered rebalancing rule of any kind in hindsight. Our approach lets practitioners express an a priori view that one of the favored asset allocations (“bets”) b ∈ {b1,...,bn} will turn out to have performed spectacularly well in hindsight. In limiting our robustness to some discrete set of asset allocations (rather than all possible asset allocations) we reduce the price of the rebalancing option and guarantee to achieve a correspondingly higher percentage of the hindsight-optimized wealth at the end of the planning period. A practitioner who lives to delta-hedge this variant of Cover’s rebalancing option through several decades is guaranteed to see the day that his realized compound-annual capital growth rate is very close to that of the best of the discrete set of rebalancing rules in hindsight. Hence the point of the rock-bottom option price.
2019-03-03T00:00:00ZSuper-Replication of the Best Pairs Trade in HindsightGarivaltis, Alexhttps://commons.lib.niu.edu/handle/10843/193352019-02-19T14:12:17Z2019-01-11T00:00:00ZSuper-Replication of the Best Pairs Trade in Hindsight
Garivaltis, Alex
This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing rule will sell a precise amount of the outperforming stock and put the proceeds into the underperforming stock.
Under typical conditions, in hindsight one can find pairs rebalancing rules that would have spectacularly beaten the market. Our trading strategy, which extends Ordentlich and Cover’s (1998) “max-min universal portfolio,” guarantees to achieve an acceptable percentage of the hindsight-optimized wealth, a
percentage which tends to zero at a slow (polynomial) rate. This means that on a long enough investment horizon, the trader can enforce a compound-annual growth rate that is arbitrarily close to that of the best pairs rebalancing rule in hindsight. The strategy will “beat the market asymptotically” if there turns
out to exist a pairs rebalancing rule that grows capital at a higher asymptotic rate than the market index.
The advantages of our algorithm over the Ordentlich and Cover (1998) strategy are twofold. First, their strategy is impossible to compute in practice. Second, in considering the more modest benchmark (instead of the best all-stock rebalancing rule in hindsight), we reduce the “cost of universality” and achieve
a higher learning rate.
2019-01-11T00:00:00ZMultiple-Output Production and Pricing in Electric UtilitiesKarlson, Stephen H.https://commons.lib.niu.edu/handle/10843/132952018-03-06T19:12:31Z1986-07-01T00:00:00ZMultiple-Output Production and Pricing in Electric Utilities
Karlson, Stephen H.
1986-07-01T00:00:00Z