Markets: A Rigorous Course

Summary of key results

Foundation about 10 min
Result Formula
Call auction schedules D(p)=∑bj≥pqjD(p) = \sum_{b_j \ge p} q_j, S(p)=∑ak≤prkS(p) = \sum_{a_k \le p} r_k, V(p)=min⁡(D,S)V(p) = \min(D,S) (1.1)–(1.2)
Proposition 1.1 arg⁡max⁡V∈{p−,p∗}\arg\max V \in \{p^-, p^*\}, p∗=min⁡{p:S(p)≥D(p)}p^* = \min\{p: S(p) \ge D(p)\}; tie-breaks: min ∣D−S∣\lvert D-S\rvert, then closest to previous close
Cost of a round trip C=K+αB+βSC = K + \alpha B + \beta S, K=2F(1+g)K = 2F(1+g), α=σb+δ+(e+ϕ)(1+g)\alpha = \sigma_b + \delta + (e+\phi)(1+g), β=σs+(e+ϕ)(1+g)\beta = \sigma_s + (e+\phi)(1+g) (1.3)
Proposition 1.2 Δ∗/P=(α+β)/(1−β)+K/((1−β)PQ)\Delta^*/P = (\alpha+\beta)/(1-\beta) + K/((1-\beta)PQ); add the spread ss for the mid (1.4)
Intraday NSE round trip, ₹1 lakh ₹82.68 = 8.27 bp (rates of 6 Nov 2026)
Delivery round trip, ₹1 lakh ₹237.82 including DP = 23.8 bp
Nifty futures, 1 lot at 25,000 ₹966 = 5.95 bp = 14.9 points
Tax STCG 20%; LTCG 12.5% above ₹1.25 lakh; intraday speculative (4-year carry-forward, speculative-only set-off); F&O non-speculative (8 years)
Index I=∑PiNifi/DI = \sum P_i N_i f_i / D (1.5)–(1.6); return =∑wiRi=\sum w_i R_i (1.7); D′=DM′/MD' = D M'/M (1.8)
Total return index TRIt=TRIt−1(It+IDt)/It−1\text{TRI}_t = \text{TRI}_{t-1}(I_t + \text{ID}_t)/I_{t-1} (1.9)
Ex-prices split Pc/kP_c/k; bonus Pcb/(a+b)P_c b/(a+b); dividend Pc−dP_c - d; TERP (NPc+nX)/(N+n)(NP_c + nX)/(N+n) (1.10)
Adjusted series multiply pre-ex prices by F=Px/PcF = P_x/P_c; dividend factor 1−d/Pc1 - d/P_c (1.12) gives the return with reinvestment at Pc−dP_c - d (1.11)

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