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CFA/CFA Rates and Return.md

@@ -4,7 +4,9 @@ documentclass: "ctexart"
 classoption: "UTF8"
 ---
 # CFA Rates and Return
+
 ## INTEREST RATES, PRESENT VALUE, AND FUTURE VALUE
+
 1. interpret interest rates as required rates of return, discount rates, or opportunity costs
 解释利率为所需的回报率，折现率或机会成本
 1. interest rate = real risk-free rate + premium
@@ -16,8 +18,11 @@ classoption: "UTF8"
 不同的复利频率
 1. calculate and interpret the effective annual rate (EAR) and annual interest rate (APR)
 计算和解释有效年利率（EAR）和年利率（APR）
+
 ## Note
+
 ### Interest Rates
+
 - Real Risk-free rate: the time preferences of individuals for current versus future real consumption.
 不考虑通货膨胀的情况下的无风险利率, 通常是美国国债利率。代表个人对现在和未来消费的偏好
 - Inflation premium: The inflation premium compensates investors for the expected erosion of purchasing power of a bond’s future cash flows due to inflation.
@@ -34,23 +39,32 @@ governmental short-term debt (T-bills) is often used as a proxy for the nominal
 美国T票的流动性溢价为零
 - Maturity risk premium: The maturity premium compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, in general (holding all else equal). The difference between the interest rate on longer-maturity, liquid Treasury debt and that on short-term Treasury debt reflects a positive maturity premium for the longer-term debt (and possibly different inflation premiums as well).
 到期风险溢价：到期风险溢价补偿投资者对债务市场价值对市场利率变化的敏感性，因为到期日延长，一般来说（其他条件不变）。较长期限的流动性美国国债利率与短期美国国债利率之间的差异反映了较长期债务的正到期溢价（以及可能的不同通货膨胀溢价）。
+
 ### FUTURE VALUE OF A SINGLE CASH FLOW
+
 - Future value (FV)
 - Present value (PV)
 - Number of periods (n)
 - Stated annual interest rate 是年利率，不是实际利率
-lump sum (一次性支付): 仍然是 $FV = PV(1+r)^n$
+lump sum (一次性支付): 仍然是$FV = PV(1+r)^n$
 Pension fund: 养老金
+
 $$
 FV = PV(1+r)^n
 $$
+
 ### NON-ANNUAL COMPOUNDING (FUTURE VALUE)
+
 LO: calculate the solution for time value of money problems with different frequencies of compounding
+
 ### Annuity (年金)
+
 - Ordinary annuity (普通年金): payments occur at the end of each period
 - Annuity due (年金): payments occur at the beginning of each period
 - Perpetuity (永续年金): an annuity with an infinite life
+
 ### Mortgage (抵押贷款)
+
 - Down payment (首付)
 - We use the equation from annuity to calculate the monthly payment
 <!-- TODO: Need Review -->
@@ -75,9 +89,9 @@ $$
 $$
 R = \frac{P_1 - P_0 + I_1}{P_0}
 $$
-- $P_0$ is the initial price
-- $P_1$ is the final price
-- $I_1$ is the income received during the period
+-$P_0$is the initial price
+-$P_1$is the final price
+-$I_1$is the income received during the period
 ### Arithmetic or Mean Return
 $$
 \bar{R_i} = \frac{1}{n} \sum_{t=1}^n R_{it}
@@ -100,9 +114,9 @@ $$
 $$
 > Steps:
 >
-> 1. Suppose the return $r$ (see it as interest rate) is unknown.
-> 2. Calculate the present value of all cash flows using the unknown return $r$.
-> 3. Solve for $r$.
+> 1. Suppose the return$r$(see it as interest rate) is unknown.
+> 2. Calculate the present value of all cash flows using the unknown return$r$.
+> 3. Solve for$r$.
 #### Time-Weighted Rate of Return
 $$
 \prod_{t=1}^n (1 + r_t) = \frac{P_n}{P_0}
@@ -157,8 +171,8 @@ $$
 $$
 R_L = \frac{\text{Portfolio Return}}{\text{Investor's Equity}} = \frac{R_P(V_E + V_B)-V_B r_D}{V_E} = R_P + \frac{V_B}{V_E}(R_P - r_D)
 $$
-- $R_L$: leverage return
-- $R_P$: portfolio return 投资组合回报率
-- $V_E$: investor's equity 投资者的股权
-- $V_B$: borrowed funds 借来的资金
-- $r_D$: cost of borrowed funds 借来的资金的成本
+-$R_L$: leverage return
+-$R_P$: portfolio return 投资组合回报率
+-$V_E$: investor's equity 投资者的股权
+-$V_B$: borrowed funds 借来的资金
+-$r_D$: cost of borrowed funds 借来的资金的成本

CFA/Corporate Issuers/Breakeven_Point.md

@@ -4,16 +4,20 @@ documentclass: "ctexart"
 classoption: "UTF8"
 ---
 # Breakeven point
-## $Q_{\text{BE}}$ (Breakeven point)
+
+## $Q_{\text{BE}}$(Breakeven point)
+
 NI 等于 0 时的销量。
 $$
 Q_{\text{BE}} = \frac{F + C}{P - V}
 $$
-- $F$ = 固定运营成本
-- $C$ = 固定财务成本
-- $P$ = 单位价格
-- $V$ = 单位变动成本
+
+-$F$= 固定运营成本
+-$C$= 固定财务成本
+-$P$= 单位价格
+-$V$= 单位变动成本
 Operating breakeven point
+
 $$
 Q_{\text{OBE}} = \frac{F}{P - V}
 $$

CFA/Corporate Issuers/Capital_Structure.md

@@ -4,21 +4,29 @@ documentclass: "ctexart"
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 ---
 # Capital Structure
+
 ## 周期
+
 ## MM model (Modigliani-Miller)
+
 ### Assumptions
+
 - Homogeneous expectations 一致的预期
 - Perfect capital markets 完美的资本市场 (no taxes, no transaction costs, no bankruptcy costs, everyone has the same information)
 - 借款按照 risk-free rate 借
 - No agency costs 代理成本
 - Indepedent Decision 融资和投资决策是独立的
+
 ### 四种情况
+
 | | 无税 | 有税 |
 | --- | --- | --- |
 | I | 1 | 3 |
 | II | 2 | 4 |
+
 1. 无论公司的资本结构如何，价值都是一样的
 2. 价值也是一样的
+
 $$
 V_L = V_U
 $$
@@ -28,31 +36,45 @@ $$
 $$
 r_e E + r_d D = r_0 (E + D)
 $$
-3. $V_L = V_U + t D$
-4. $r_e = r_0 + \frac{D}{E} \times (r_0 - r_d) \times (1 - t)$
+
+3.$V_L = V_U + t D$
+4.$r_e = r_0 + \frac{D}{E} \times (r_0 - r_d) \times (1 - t)$
+
 $$
 V_L = V_U + t D - PV (financial distress costs)
 $$
 3 / 4 负债的成本会比权益的成本低
+
 ### reflection on MM model
+
 - Direct cost
   - bankruptcy cost
 - Indirect cost
   - agency cost
+
 ## Optimal Capital Structure
+
 $$
 V_L = V_U + t D - PV
 $$
+
 ### Target Capital Structure
-达到最优的资本结构时 ($V_L$ 最大)
+
+达到最优的资本结构时 ($V_L$最大)
+
 ### Methods to estimate the target capital structure
+
 - Market value weights
 - Examine trends
 - Peer group comparison
+
 ## Factors that influence the capital structure decision
+
 - Financing Capital Investment 机会转瞬即逝
 - Market conditions 股价之类的
 - Information asymmetry 信息不对称
 - Pecking order theory 融资的顺序
+
 ## Agency Costs
+
 - agency 和 principal 之间的冲突

CFA/Corporate Issuers/Cost_of_Capital.md

@@ -4,25 +4,31 @@ documentclass: "ctexart"
 classoption: "UTF8"
 ---
 # Cost of Capital
+
 1. WACC (Weighted Average Cost of Capital)
 2. Cost of Different Sources of Capital
 3. Estimating Beta
 4. Flotation Costs
+
 ## WACC (Weighted Average Cost of Capital)
+
 $$
 WACC = \frac{E}{V} \times r_e + \frac{D}{V} \times r_d \times (1 - T_c) + \frac{P}{V} \times r_p
 $$
 这里每一项都是边际值
-- $E$: market value of equity
-- $D$: market value of debt
-- $V$: total market value of equity and debt
-- $r_e$: cost of equity
-- $r_d$: cost of debt
-- $T_c$: corporate tax rate
-- $P$: market value of preferred stock
-- $r_p$: cost of preferred stock
+
+-$E$: market value of equity
+-$D$: market value of debt
+-$V$: total market value of equity and debt
+-$r_e$: cost of equity
+-$r_d$: cost of debt
+-$T_c$: corporate tax rate
+-$P$: market value of preferred stock
+-$r_p$: cost of preferred stock
 <span style="color:red">market value</span>
+
 ## Cost of Different Sources of Capital
+
 - Debt
   - YTM (yield to maturity)
   - Debt rating 利用债券评级
@@ -31,45 +37,65 @@ $$
   - Common stock
     - CAPM
     - Bond yield plus risk premium
+
 ### YTM (yield to maturity) 折现率
+
 $$
 P_0 = \frac{PMT}{1 + YTM} + \frac{PMT}{(1 + YTM)^2} + \cdots + \frac{PMT + FV}{(1 + YTM)^n}
 $$
-- $P_0$: current price
-- $PMT$: payment
-- $FV$: face value
-- $n$: number of periods
+
+-$P_0$: current price
+-$PMT$: payment
+-$FV$: face value
+-$n$: number of periods
+
 ### Preferred Stock
+
 $$
 r_p = \frac{D}{P}
 $$
-- $D$: dividend
-- $P$: price <span style="color:red">market value</span>
+
+-$D$: dividend
+-$P$: price <span style="color:red">market value</span>
+
 ### CAPM (Capital Asset Pricing Model)
+
 $$
 E(R_i) = R_f + \beta_i \times (E(R_m) - R_f)
 $$
-- $E(R_i)$: expected return
-- $R_f$: risk-free rate
-- $\beta_i$: the return sensitivity of stock $i$ to changes in the market return: 股票的市场敏感性
-- $E(R_m)$: expected return of the market
+
+-$E(R_i)$: expected return
+-$R_f$: risk-free rate
+-$\beta_i$: the return sensitivity of stock$i$to changes in the market return: 股票的市场敏感性
+-$E(R_m)$: expected return of the market
+
 ### Bond yield plus risk premium
+
 $$
 r_e = r_d + \text{risk premium}
 $$
-- $r_d$: cost of debt 税前
+
+-$r_d$: cost of debt 税前
+
 ## Estimating Beta
+
 ### Unpublished or thinly traded companies
+
 Two components
+
 - 财务风险
 - 属性风险
 找到一个相似的公司
+
 $$
 \beta_U = \beta_E \times \frac{1}{1 + (1 - t) \frac{D}{E}} \\
 \beta_E = \beta_U \times (1 + (1 - t) \frac{D}{E})
 $$
-- $\beta_U$ : unlevered beta
-- $\beta_E$ : levered beta
+
+-$\beta_U$: unlevered beta
+-$\beta_E$: levered beta
+
 ## Flotation Costs
+
 - First way: incorporate the flotation costs into the cost of capital, 利用高登模型
 - Second way: deduct the flotation costs from the initial cash flow, 利用调整后的现金流

CFA/Corporate Issuers/Financial Risk and Financial Leverage.md

@@ -4,10 +4,15 @@ documentclass: "ctexart"
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 ---
 # Financial Risk and Financial Leverage
+
 ## Financial Risk
+
 债的利息
+
 ### DFL (Degree of Financial Leverage)
+
 $$
 \textrm{DFL} = \frac{\text{percentage change in NI}}{\text{percentage change in EBIT}} = \frac{\frac{\Delta \text{NI}}{\text{NI}}}{\frac{\Delta \text{EBIT}}{\text{EBIT}}}= \frac{Q(P-V) - F}{Q(P-V) - F - C}
 $$
-- $C$ = 固定的财务成本
+
+-$C$= 固定的财务成本

CFA/Corporate Issuers/Operating Risk and Operating Leverage.md

@@ -4,22 +4,30 @@ documentclass: "ctexart"
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 ---
 # Operating Risk and Operating Leverage
+
 ## Operating Risk
+
 - 如果有固定成本，那么就有风险
 - 固定成本/可变成本越大，风险越大
+
 ## Operating Leverage
+
 DOL (Degree of Operating Leverage)
+
 ### 定义式
+
 $$
 DOL = \frac{\% \Delta EBIT}{\% \Delta Sales}
 $$
 单位销量的变化导致Operating Income的变化
+
 ### 计算式
+
 $$
 DOL = \frac{Q(P - V)}{Q(P - V) - F} = \frac{sale - \text{TVC}}{sale - \text{TVC} - F}
 $$
-- $Q$: quantity
-- $P$: price per unit
-- $V$: variable cost per unit
-- $F$: fixed cost
-- $\text{TVC}$: total variable cost
+-$Q$: quantity
+-$P$: price per unit
+-$V$: variable cost per unit
+-$F$: fixed cost
+-$\text{TVC}$: total variable cost