RDP 9307: Explaining Forward Discount Bias: Is it Anchoring? Tables and Figures

David W. R. Gruen and Marianne C. Gizycki

June 1993

Table 1: Interest Differentials and Estimates of θ
Country Pair Mean Interest
Differential (% p.a) 		Standard Deviation of
Interest Differ. (% p.a) 		θ (4-week periods)
UK-US ('79–'91) 2.9 2.8 12.3
Ger-US ('79–'91) −1.9 1.8 6.9
Jap-UK ('81–'91) −5.6 2.0 12.9
Jap-Ger ('81–'91) −0.9 1.9 26.3
Jap-US ('81–'91) −2.7 2.2 17.4
Table 2: Values of the Parameters in the Model
θ (periods) λ (periods) σm (per period) σe (per period) β (per period)
6 6.4 0.0052 0.031 0.17 (weakly anchored)
1.50 (strongly anchored)
50 18.2 0.0053 0.031 0.02 (weakly anchored)
0.18 (strongly anchored)
Table 3: Model Results
Long-run averages of the proportion of anchored traders, Inline Equation and the coefficient
on the forward discount,Inline Equation, from the regression Δst+1 = Inline Equation fdt+εt+1
θ Investors' horizon (Years) Markov chain para-meter All anchored traders are weakly anchored (β = 1/θ) All anchored traders are strongly anchored (β = 9/θ)
q Inline Equation Inline Equation Inline Equation Inline Equation
6
periods
(24 weeks)		 One 0.1 0.37 0.23 0.22 −0.13
0.3 0.42 0.14 0.33 −0.17
0.5 0.44 0.09 0.40 −0.13
1.0 0.45 0.06 0.45 0.06
Three 0.1 0.27 0.45 0.14 0.11
0.3 0.35 0.28 0.25 0.02
0.5 0.39 0.19 0.34 0.00
1.0 0.42 0.13 0.42 0.13
Ten 0.1 0.18 0.63 0.08 0.37
0.3 0.26 0.46 0.17 0.24
0.5 0.31 0.35 0.25 0.20
1.0 0.37 0.23 0.37 0.23
50
periods
(200 weeks)		 One 0.1 0.51 0.31 0.34 0.09
0.3 0.48 0.34 0.41 0.11
0.5 0.50 0.31 0.46 0.18
1.0 0.50 0.32 0.50 0.32
Three 0.1 0.43 0.41 0.24 0.21
0.3 0.45 0.39 0.35 0.19
0.5 0.48 0.35 0.41 0.24
1.0 0.47 0.36 0.47 0.36
Ten 0.1 0.31 0.58 0.13 0.41
0.3 0.37 0.50 0.25 0.34
0.5 0.41 0.44 0.33 0.34
1.0 0.43 0.41 0.43 0.41
Table 4: Comparison with McCallum's (1992) Results
Variables
(Regression No.)		 OLS estimates
(OLS std.errors)
Constant Slope		 R2 S E D-W
st – st−1 on
ft−1 – st−1
(1)		 Data −0.016 −4.30      
  (0.006) (1.70) 0.041 0.035 2.19
Model 0.001 −0.11      
  (0.001) (0.46) 0.000 0.032 2.05
st on ft (2) Data −0.003 1.001      
  (0.001) (0.001) 1.000 0.002 0.37
Model 0.000 1.000      
  (0.000) (0.000) 1.000 0.002 0.31
st on ft−1 (3) Data −0.009 0.990      
  (0.012) (0.016) 0.963 0.036 2.05
Model 0.002 0.998      
  (0.001) (0.002) 0.995 0.032 2.03
Δst on Δft (4) Data 0.000 1.002      
  (0.000) (0.002) 0.999 0.001 1.60
Model 0.000 1.002      
  (0.000) (0.001) 0.999 0.001 2.23
Δst on Δft−1 (5) Data 0.002 −0.063      
  (0.003) (0.082) 0.004 0.036 1.96
Model 0.001 −0.023      
  (0.001) (0.022) 0.001 0.032 2.00
st – st−2 on
ft−1 – st−2
(6)		 Data −0.001 0.940      
  (0.003) (0.083) 0.461 0.036 1.93
Model 0.001 0.977      
  (0.001) (0.022) 0.487 0.032 1.99
st – st−3 on
ft−1 – st−3
(7)		 Data −0.002 1.054      
  (0.003) (0.061) 0.670 0.036 2.18
Model 0.001 1.003      
  (0.001) (0.016) 0.661 0.032 2.04

Data are McCallum's results for $/DM, monthly 1978:1 to 1990:7. Model results are based on a 2000 period simulation assuming investors' horizon is one year, q = 0.1, θ = 6 and strongly anchored traders (β = 9/θ).

Figure 1: 4-Week Change in $US/$A Compared with Estimates of the Change
Figure 2: Exchange Rate Response to Domestic Monetary Expansion
Figure 3: Probability that Anchored Portfolio Outperforms Rational Portfolio over Investors' Horizon (Strongly Anchored Traders: θ = 6).