Efficiency impact of convergence bidding in the california electricity market

Abstract

The California Independent System Operator (CAISO) has implemented Convergence Bidding (CB) on February 1, 2011 under Federal Energy Regulatory Commission’s September 21, 2006 Market Redesign and Technology Upgrade Order. CB is a financial mechanism that allows market participants, including electricity suppliers, consumers and virtual traders, to arbitrage price differences between the day-ahead (DA) market and the real-time (RT) market without physically consuming or producing energy. In this paper, market efficiency is defined in terms of trading profitability, where a zero-profit competitive equilibrium implies market efficiency (Jensen in, J Financial Econ 6(2):95–101, 1978). We analyze market data in the CAISO electric power markets, and empirically test for market efficiency by assessing the performance of trading strategies from the perspective of virtual traders. By viewing DA–RT spreads as payoffs from a basket of correlated assets, we can formulate a chance constrained portfolio selection problem, where the chance constraint takes two different forms as a value-at-risk constraint and a conditional value-at-risk constraint, to find the optimal trading strategy. A hidden Markov model (HMM) is further proposed to capture the presence of the time-varying forward premium. This is meant to be a contribution to the modeling of regime shifts in the electricity forward premium with unobservable states. Our backtesting results cast doubt on the efficiency of the CAISO electric power markets, as the trading strategy generates consistent profits after the introduction of CB, even in the presence of transaction costs. Nevertheless, by comparing with the performance before the introduction of CB, we find that the profitability decreases significantly, which enables us to identify the efficiency gain brought about by CB. Convincing evidence for the improvement of market efficiency in the presence of CB is further provided by the test for the Bessembinder and Lemmon (J Finance 57(3):1347–1382, 2002) model.

Appendices

Appendix 1

With $\phi (u) = (u+1)_+^2$, we can show $\phi (\frac{u}{\alpha }) \ge {I} (u \ge 0)$ for any $\alpha >0$. By substituting $u=- R_t^T y_t -\gamma$, we have $\phi ( \frac{1}{\alpha }(- R_t^T y_t -\gamma ) ) \ge {I}( - R_t^T y_t -\gamma \ge 0)$. Taking expectation on both sides yields,

$$\begin{aligned} E\left[ \phi \left( \frac{1}{\alpha }(- R_t^T y_t -\gamma )\right) \right] \ge P( - R_t^T y_t -\gamma \ge 0). \end{aligned}$$

(36)

By multiplying $\alpha$ on both sides and replacing the positive part function, we can further show a conservative approximation of $P( - R_t^T y_t -\gamma \ge 0) \le 1-\eta$ in the following form,

$$\begin{aligned} \alpha P(- R_t^T y_t -\gamma \ge 0)\le & {} \alpha E \left[ \phi \left( \frac{1}{\alpha }(- R_t^T y_t -\gamma ) \right) \right] \end{aligned}$$

(37)

$$\begin{aligned}= & {} \alpha E \left[ \left( \frac{1}{\alpha }(- R_t^T y_t -\gamma ) + 1 \right) _+^2 \right] \end{aligned}$$

(38)

$$\begin{aligned}\le & {} \alpha E \left[ \left( \frac{1}{\alpha }(- R_t^T y_t -\gamma ) + 1 \right) ^2 \right] \end{aligned}$$

(39)

$$\begin{aligned}\le & {} \alpha (1-\eta ). \end{aligned}$$

(40)

Rearranging $\alpha E[ ( \frac{1}{\alpha }(- R_t^T y_t -\gamma ) + 1 )^2 ] \le \alpha (1-\eta )$ yields,

$$\begin{aligned}&\alpha E \left[ \left( \frac{1}{\alpha }(- R_t^T y_t -\gamma ) + 1 \right) ^2 \right] -\alpha (1-\eta ) \end{aligned}$$

(41)

$$\begin{aligned}&\quad = \frac{1}{\alpha } E\left[ \left( R_t^T y_t +\gamma \right) ^2\right] -2 E\left[ \left( R_t^T y_t +\gamma \right) \right] + \eta \alpha \le 0 . \end{aligned}$$

(42)

Noticing that (42) is a quadratic function, we can minimize the function by setting $\alpha = \left( \frac{1}{\eta } E\left[ \left( R_t^T y_t+ \gamma \right) ^2\right] \right) ^{\frac{1}{2}}$.²¹ By substituting $\alpha = \left( \frac{1}{\eta } E\left[ (R_t^T y_t+ \gamma )^2\right] \right) ^{\frac{1}{2}}$ into (42), we derived the Chebyshev bound,

$$\begin{aligned} -E \left[ \left( R_t^Ty_t +\gamma \right) \right] + \left( \eta E\left[ \left( R_t^Ty_t +\gamma \right) ^2 \right] \right) ^{\frac{1}{2}} \le 0 . \end{aligned}$$

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Appendix 2

See Tables 12, 13, 14, 15, 16, 17 and 18.

Table 12 Summary statistics for Pre-CB DA–RT Spreads

Table 13 Seasonal means of Pre-CB DA–RT spreads

Table 14 Seasonal standard deviations of Pre-CB DA–RT spreads

Table 15 Transition probabilities of the pre-CB GMHMM (one-step)

Table 16 Cluster probabilities of the pre-CB GMHMM

Table 17 Summary statistics for DA–RT spreads in the clusters of the pre-CB GMHMM

Table 18 Summary statistics for DA–RT spreads in the states of the pre-CB GMHMM

Appendix 3

See Figs. 14, 15, 16 and 17.

Fig. 14

Pre-CB within-cluster sum of squared error

Fig. 15

Pre-CB posterior state probability

Fig. 16

Marginal distribution of Pre-CB DA–RT spreads for 1 a.m

Fig. 17

Marginal distribution of Pre-CB DA–RT spreads for 1 p.m