Summary of key results

Result	Formula
Bond price	$P=\sum_k CF_k(1+y/m)^{-mt_k}$ (11.2)
YTM uniqueness	$P(y)$ strictly decreasing and convex (Prop. 11.1)
Macaulay duration	$D_{\text{mac}}=\sum t_k PV_k/P$ (11.4)
Modified duration	$D_{\text{mod}}=-P'/P=D_{\text{mac}}/(1+y/m)$ (Prop. 11.2)
Par bond	$D_{\text{mod}}=(1-(1+j)^{-N})/j$ periods (11.6)
Convexity	$C=P^{-1}\sum t_k(t_k+1/m)CF_k(1+y/m)^{-mt_k-2}$ (11.8)
Price change	$\Delta P/P\approx -D_{\text{mod}}\Delta y+\tfrac12C\Delta y^2$ (11.9)
Equity duration	$D_{\text{mod}}^{eq}=1/(r-g)=P/D_1$ ; $D_{\text{mac}}^{eq}=(1+r)/(r-g)$ (11.11)
Fisher / breakeven	$(1+i)=(1+r)(1+\pi^e)$ ; $b=i-r^{\text{TIPS}}$ (11.12–13)
Term premium	$y_n=\frac1n\sum\mathbb E r_{t+k}+TP_n$ (11.14a)
Taylor rule	$i=r^+\pi+0.5(\pi-\pi^)+0.5x$ (11.15); stable iff $a_\pi>0$
CIP	$F=S(1+r_dT)/(1+r_fT)$ ; band $[L,U]$ (11.17–18)
Fama regression	$\Delta s_{t+1}=a+b(f_t-s_t)+\varepsilon$ ; $b<0\Rightarrow \text{Cov}(p,q)<-\text{Var}(q)$ (11.20–21)
Carry	$xr=(i-i^*)-\Delta s$ (11.22)
DXY	geometric, EUR weight 57.6% (11.23)
USD return of FPI	$1+R_{\$}=(1+R_{\text{₹}})S_0/S_1$ (11.24)
Inflation and P/E	$P/D_1=1/(\rho-g_r+(1-\lambda)\pi)$ (11.25)
Debt dynamics	$d_{t+1}=d_t(1+i)/(1+g_n)-pb_t$