As the U.S. electric power industry unbundles, the industry and its regulators grapple with two big questions concerning the degree to which distribution services should be unbundled. First, what...

## Getting It Right: The *Real* Cost Impacts of a Renewables Portfolio Standard

expect that the cost of such strategies will rise or the risk will increase. In any event, all the hedging strategies notwithstanding, somewhere in the system there will remain risk, which someone will have to absorb at some point. And ultimately, if energy prices rise precipitously, the system will collapse with declarations of force majeure - as was the case during the hot spell of 1998 to 1999. Except where risk is purely random and widely diversified, e.g., among numerous, large multi-national insurance firms, such results are to be expected. Indeed the industry's history includes the abrogation of fixed-price long-term nuclear fuel contracts by Westinghouse and others when the cost of "yellowcake" (a uranium-based feed material) rose sharply in the 1970s.

History validates the common wisdom that, when you have a fixed-price long-term contract, you have exactly that ¼ a contract. From a national policy perspective, therefore, incorporating riskless physical assets such as PV and wind may be essential for long-term energy security and reliability.

Shimon Awerbuch, Ph.D., is an independent financial economist in Nashua, N.H. He, along with Leonard Hyman, CFA, and Andrew Vesey, is the author of Unlocking the Benefits of Restructuring: A Blueprint for Transmission, Public Utilities Reports Inc., 1999. Contact Dr. Awerbuch at Awerbuch@aol.com.

This research was supported in part by a grant from the Interstate Renewable Energy Council ( www.irecusa.org/). The author thanks Jane Weissman for her support and Richard Bower, Ronald Lehr and Adam Serchuk for their helpful comments. The views expressed do not necessarily reflect the position of IREC or the U.S. Department of Energy

The Math Fundamentals of Portfolio Theory

Portfolio theory generally is attributed to Harry Markowitz[Fn.27] who recognized that by considering the co-movement (co-variance) of returns, risky and riskless assets can be assembled in such a way as to increase expected returns with little or no additional risk. The theory was conceived in the context of financial portfolios, where it relates rp, the expected portfolio return, to sp, the total portfolio risk, which is defined as the standard deviation of those returns. The relationship is illustrated below using a portfolio of two risky assets. The expected portfolio return, rp, is the weighted average of the individual returns of the two securities:

E(rp) = x1 • E(r1) + x2 • E(r2) (1)

Where:

E(rp) is the expected portfolio return; x1, x2 are the proportions of the portfolio in assets 1 and 2; andE(r1), E(r2) are the expected returns for assets 1 and 2;[Fn.28]

The overall portfolio risk, sp, also is a weighted average of the two securities, but is tempered by the correlation coefficient between the two returns:

sp = SQRT { x12 s12 + x22 s22 + 2x1x2r1,2 s1s2 } (2)

Where:

r1,2 is the correlation coefficient between the two return streams, and s1 and s1 are the standard deviations of the periodic (e.g. ,annual) returns for asset 1 and 2 respectively.

The introduction of riskless assets (such as Treasury bills) into the portfolio reduces Equation (2) to a line. Consider a portfolio of a risky security (e.g. ,common stock)