The name is absent

long term maturity ( n )
6      12     24     36     60     120

reg 1  mean(β) 0.9836 0.9792 0.9814 0.9871  0.9954  1.0104

stdev(β) 0.0472 0.0496 0.0529 0.0518 0.0578 0.0434

reg 2  mean(β) 0.7904 0.9628 0.9930 0.9651  0.9748 0.9848

stdev(β) 0.4327 0.0530 0.0701  0.0776 0.0689 0.0494

linear mean(β) 0.4151  0.5671  0.6323 0.8385 0.9929 0.9401

stdev(β) 0.6603 0.4427 0.5608 0.7087 0.6486 0.5103

Linear model rolling 60 obs; regimes 1 and 2 rolling 50 obs

Table 8

A financial interpretation rationalizes our empirical results. Campbell argues that a large bias
downward of the estimated slope coefficient is due to a small variance of the rationally expected
changes in short rates relative to the variance of the term premium. That is, the expectations theory
holds when investors are well informed about future movements in short rates.

According to Campbell and Shiller (1991) we can decompose the spread into into an expectational
component (theoretical spread) and the term premium:

n-m

m

∑Ei^m

t t + mq

q=0

(11)

= thsp_t^n,m + tp_t^n,m

The variance of the spread depends on the variance of both its components plus twice their

24
covariance :

n m                  n,m              n,m                      n,m     n,m

var u_t — it j= varuripj_t ∫+ var ∖ip_t ∫+ 2∙ cov urisp_t , tpt ∫ =

(12)

n      m        nm

= ^var{it}^{+ var}{it }^{- 2} ∙ ^cov{it^{, i}t }

As shown in the bottom panel of Table 9, in the single regime model for n ≤ 36, the standard
deviation of the expectational component is lower than the standard deviation of the term premium,
the slope estimate is thus strongly biased downward (far below unity, as shown in the right panel of
Table 6). In the threshold framework this result is inverted. In each regime the variability of the
term premium, as measured by its standard deviation, is much lower than the variability of the

²⁴ The covariance between the theoretical spread and the term premium is negative. At short maturities (n =12, 6) the
covariance is close to zero, but still negative. The covariance between long and short term rates is positive. The
covariance is a negative function of the distance between maturities (n - m). The variance of short term yields is
generally larger than the variance of long term yields.

24

<<   22   23   24   25   26   27   28   >>

More intriguing information