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财经·职业
22
engines
货币时间价值 · 复利增长
Time value of money · compound growth
FV = PV·(1+r)^t · 约 72/r 年翻一倍(72 法则)
FV = PV·(1+r)^t · doubles in ≈ 72/r years (rule of 72)
债券价格 与 收益率
Bond price vs yield
收益率上升价格下降(凸性)· 收益率=票息率时平价(100)
Price falls as yield rises (convex) · at yield=coupon the bond trades at par (100)
期权到期收益图
Option payoff at expiry
收益 随 标的价格 · 内在价值 减 权利金
Profit vs underlying price · intrinsic value minus premium
供给与需求 · 市场均衡
Supply & demand · market equilibrium
价格稳定在需求量等于供给量的那一点
Price settles where the quantity demanded equals the quantity supplied
盈亏平衡分析(本量利)
Break-even analysis (CVP)
当收入在 Q = FC/(P−VC) 处超过总成本,才开始盈利
Profit starts once revenue overtakes total cost at Q = FC/(P−VC)
CAPM · 证券市场线
CAPM · the Security Market Line
要求收益率 = 无风险利率 + β × 市场风险溢价
Required return = risk-free rate + β × market risk premium
净现值 NPV 与 内部收益率 IRR
NPV & IRR · capital budgeting
折现率越高 NPV 越低;NPV 为零处即内部收益率 IRR
NPV falls as the discount rate rises; IRR is where NPV = 0
关键路径法(CPM)
Critical path (CPM)
相互依赖活动中最长的一条链,决定项目最短完成时间
The longest chain of dependent tasks sets the shortest possible project time
有效前沿 · 投资组合
Efficient frontier · portfolio choice
两种资产的组合可把风险降到平均值以下 —— 分散化
Mixing two assets can cut risk below the average — diversification
杜邦分析 · ROE 分解
DuPont analysis · ROE breakdown
净资产收益率 = 盈利能力 × 营运效率 × 财务杠杆
ROE = profitability × efficiency × leverage
无差异曲线与预算线
Indifference curves & budget line
Cobb-Douglas U=xᵃyᵇ · 预算线 · MRS=Px/Py 相切最优
Consumer optimum where MRS = price ratio · Cobb-Douglas U = xᵃ·yᵇ
厂商成本曲线
Firm cost curves
FC/VC → AFC/AVC/ATC/MC · MC 过最低点 · 停业/盈亏点
MC through the minima of AVC and ATC · shutdown & break-even
等产量线与等成本线
Isoquants & isocost
等产量线 + 等成本线 · MRTS=w/r · 规模报酬
Least-cost input mix where MRTS = w/r · Cobb-Douglas Q = A·Kᵅ·Lᵝ
IS-LM 模型
IS-LM model
IS × LM 交点 · 均衡 Y*,r* · 财政/货币政策移动
Solve output & the interest rate where the goods and money markets both clear
总需求—总供给（AD-AS）
Aggregate demand & supply (AD-AS)
AD/SRAS/LRAS · 短期长期均衡 · 产出缺口/冲击
Short-run equilibrium, the output gap vs potential, and long-run self-correction
垄断与完全竞争
Monopoly vs perfect competition
P=a−bQ, MR=MC · 垄断 vs 竞争 · 无谓损失 DWL
MR = MC sets the monopoly output; the deadweight loss triangle vs the competitive benchmark
博弈论 · 2×2 收益矩阵
Game theory · 2×2 payoff matrix
2×2 收益矩阵 · 最佳反应/占优 · 纳什均衡
Best-response analysis · pure-strategy Nash equilibrium · dominant strategies
经济订货批量(EOQ)
Economic Order Quantity (EOQ)
EOQ=√(2DS/H) · 订货 vs 持有成本 · 最优批量
Balancing ordering cost against holding cost · optimal lot size
M/M/1 排队系统
M/M/1 queue
ρ=λ/μ · L/Lq/W/Wq · 队长分布 Pₙ
Single-server queue · utilization ρ · queue length L · waiting time W
线性规划 · 图解法
Linear programming · graphical method
约束半平面 → 可行域 · 目标函数线 · 最优顶点
Shade the feasible region, slide the objective line to the optimal vertex
Black-Scholes 期权希腊字母
Black-Scholes option Greeks
Black-Scholes · Δ/Γ/Θ/vega/ρ · 看涨看跌定价
European call/put pricing and its sensitivities (the Greeks)
债券久期与凸性
Bond duration & convexity
Macaulay/修正久期 · 凸性 · 价格-收益率曲线
Price sensitivity to yield: duration is the slope, convexity is the curvature