Un-levering and Re-levering Betas. p. 1 of 1.
Dick Sweeney
Un-levering Betas, and Re-levering Betas
Market Model. The dependent variable: the rate of return on the Morgan Stanley index of the
Jakarta Stock Exchange (JSE), in USD. Regress this against the rate of return on “the” world
market in USD, where the Morgan Stanley world index is used as a proxy for the world
market—Corning believes its shareholders are well diversified across the world market. The
usual market model is
RJ,t = a + b RWM,t + ut.
RJ,t is the rate of return on the JSE in USD, RWM,t is the rate of return on the world market in
USD, and ut is a mean-zero, uncorrelated random error; a and b are parameters to be fit by OLS.
Morgan Stanley JSE data start in 1988. The goal is to find an estimated slope, b̂ , to use as an
estimate of  in the CAPM. Suppose that the estimated beta is 0.50, b̂ JSE = 0.50.
Unlevering a Beta. Estimated betas are likely to have leverage different from the leverage
planned for the project. One backs out the unlevered beta from the index’s estimated beta. Thus,
if the JSE beta is 0.50 and the average debt-value ratio for JSE firms is 40%, one unlevers the
estimated beta of 0.50 to find the beta for the unlevered index.
Unlevering a beta can be complicated. A simple, workable procedure assumes that the debt beta
is zero. The index’s overall beta is a weighted average of its stock and debt betas,
index,over = (S/V) S,L + (D/V) (1 - t) D,L
If D/V = 0.40 for the average Indonesia firm in the index, then S/V = 0.60. The estimated levered
equity beta is estimated to be S,L = 0.50 from the market model. By assumption, D,L = 0.0.
Thus,
index,over = (S/V) S,L = .60 x .50 = .30.
Thus, the asset beta is 0.30. Note that if the firm is unlevered, then S/V = 1. Thus, index,over =
(S/V) S,U = S,U. The asset beta is also the unlevered share beta; here, the unlevered beta is 0.30.
Relevering a Beta. Consider the equity beta for the levered IAI project, where D/V = .6 and S/V
= .4. From
project = (S/V) S,L + (1 - t) (D/V) D,L = 0.30 = 0.40 S,L, or
S,L = 0.30/0.40 =
0.75.
IAI has D/V = .6—rather than D/V = 0.4, as assumed for the average firm in the JSE
index. Thus, IAI’s levered equity beta is 0.75 rather than the 0.50 estimated for the JSE index.