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FINANCE - Coggle Diagram

- - - - A portfolio is a collection of investment assets
      - Asset allocation refers to the choice between broad asset classes
      - Security selection refers to the choice of assets within each asset class (IBM, TSLA …)
      - Security analysis involves the valuation of particular securities that might be included in the portfolio
  - - - Firms: Net demanders of capital. Raise capital to invest in real assets Households: Net suppliers of capital. Purchase securities issued by firms that need to raise capital Governments: Can be both. Since WW2 US government has been demander
        
        Financial Intermediaries- pool funds and invest
        
        Investment companies (mutual funds, hedge funds)
        
        Banks
        
        Insurance companies
        
        Credit unions
        
        Venture Capital and Private Equity- Some firms are too small to raise capital from the stock or bond markets -> rely on bank loans and private investors who invest in return for an ownership stake in the firm (venture capital= equity investments in these firms, private equity- investments in firms not traded publically)
  - - - Treasury bills / Certificate of deposits / Commercial paper / Bankers’ acceptance / Eurodollars: Dollars time deposits in banks outside of the US / Repos and reverses- securities bought overnight to buy the next day / Federal funds / LIBOR (London Interbank Offered Rate)-Short-term loan between large banks in London (€STR (Euro Short-Term Rate))
    - - Treasury notes and bonds: Issued by the government with maturities ranging up to 10 years (notes) or between 10 and 30 years (bonds), Inflation-protected treasury bonds (TIPS), International bonds, Corporate bonds, Mortgages and mortgage-backed securities
        
        Types of stock
        
        Common stock/ equities- represents ownership shares in a corporation -> rights: voting, share of financial benefits, limited liability -> residual claim: in case of liquidation the holders are last in line
        
        Preferred stock- hybrid between debt and equity -> Promises a fixed payment stream (bonds) and also does not convey voting rights
        Preferred stockholder have priority over common stockholders and tax treatment is different
        
        Stock market indices: Dow Jones Industrial Average (30 large blue-chip), S&P500 (broad based index top 500 firms -market proxy)
        
        Derivate market
        
        Options: Gives its holder the right to purchase (call) an asset for a specified price (strike price), before or on a specified future date (put option- gives the right to sell) (you can buy but you don’t have to “have an option”)
        Futures: Require its holder to purchase an asset for a specified price on a specified future date (obligation to buy)
- - - - The payback period is the amount of time it takes to recover the initial investment. The project is accepted if the payback period is less than the benchmark, otherwise it is rejected
  - - - Effects of new products
        
        Opportunity costs- indirect cost of the value a resource could have provided in the best alternative use (new product-> new housing for equipment-> new rent/ overhead)
        
        Project externalities are the indirect effects of the project that may affect the profits of other business activities of the firm
        
        Cannibalization is when the sales of the new product decrease sales of an existing project
        
        Sunk costs -costs which have been incurred regardless of whether the project is undertaken or not. They should not be included in the incremental earnings analysis (a feasibility study)
        
        Fixed overhead expenses should only be included if they are directly tied to the project (project requires additional expenses)(incremental costs and benefits should be included)
        
        Complications- Sales typically change every year, Prices also change, Average costs per unit are typically not constant over time
    - - Less Capital expenditures - buying the equipment Depreciation -a non-cash expense (adjust the free cash flows accordingly)
      - Plus: Depreciation -a non-cash expense (adjust the free cash flows accordingly)
        
        salvage value
      - Less: Net Working capital- "inventory stock up" => NWC= Current Assets - Current Liabilities= Cash + Inventory(consuming CF)+Receivables - Payables (increase CF)
      - We adjust the Unlevered net income to calculate FCF
        
        Free cash flows= (Revenues -Costs -Depreciation)(EBIT) (1-τ_C )+Depreciation-CapEx-∆NWC => ("Revenues" -"Costs" )(1-τ_C )+Depreciationτ_c (Depreciation tax shield)- CapEx -∆NWC
        
        Terminal or continuation value of the project is the market value of all free cash flows occurring after the end of the forecast horizon (aspirin)
- - - - writer profit= -(S_T - X)
    - - Profit: holder= -C....writer = C
  - - - writer profit= -(X - S_T) + P
    - - writer profit= P
  - - - Put-call parity: long call+T-bill = protective put
        
        C+ X/(1+r_f)^T = S_0 + P
  - - - C is identical for american and european oprions
        
        C ≥ S_0 - PV(X)
    - - P for american is > than european options
        
        Put-Call parity: P_e = C - S_0 + PV(X)
        
        P_American > C - S_0 + PV(X)
- - - - volatility= total risk.... systematic risk= beta -> bc market risk cant be diversified -> determinates the cost of capital
    - - risk of default & loss rate -> r_d= YTM - prob(default)*expected loss rate ..........historical average loss rate=60%
  - - - Unlevered cost of capital: r_u = (E/D+E)r_e + (D/E+D)r_d
        
        Unlevered beta: β_U=E/(D+E) β_E+D/(D+E) β_D
        
        r_U=r_wacc+(D/(E+D)) τ_C r_D
      - Net debt= Debt - Excess cash & short-term investment
      - Weighted Average Cost of Capital can evaluate projects with similar risk and the same financin
        
        r_wacc=E/(E+D) r_E+D/(E+D) r_D (1-τ_C)
  - - - debt holders must be paid before equity
        
        homemade leverage- investor choosing to borrow or lend
    - - MM 1: In a perfect capital market, the total value of a firm’s securities is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.
      - MM 2: The cost of capital of levered equity increases with the firm’s market value debt-equity ratio.......𝑟𝐸=𝑟𝑈+𝐷/𝐸(𝑟𝑈−𝑟𝐷)
        
        𝛽𝐸=𝛽𝑈+𝐷/𝐸(𝛽𝑈−𝛽𝐷)
  - - - PV(interest tax shield): permanent debt where D is constant and risk-free: PV(interest rate)= tax rate * Debt
        The debt-equity D/E ratio is constant: PV(interest tax shield)= V^L - V^U
    - - Direct costs
        
        PV(cost of financial distress)=V^U-V^L= prob * bankrupcy cost / rate
        
        debt holders pay the distress cost (dont get full payment), equity holders dont care about distress cost (nothing is paid either way)
      - Optimal capital structure
        
        V^L=V^U+PV("Interest tax shield" )-PV("Financial distress costs" )-PV("Agency costs of debt")+PV("Agency benefits of debt")
        
        Agency costs- equity holders will maximize their equity than taking a better NPV project
        
        debt capacity of an investment= amount of debt, D_t, which is required to keep a fixed debt-value ratio, d, at any point in time, t (D_t=d*V_t^L)
- - - - Prices and interest rates have an inverse relationship
      - Yield-to-maturity : YTM is a measure of the average rate of return of a bond (=YIELD(Start date,maturity d.,annual coupon rate, price, redemp at maturity % of par, frequency, day count basis 0)
        
        Realized return- actual return earned during holding period
        
        yields (or spot rates) on long-term bonds reflect the path of short rates anticipated by the market
    - - Liquidity premium: long term investors premium on the risk of holding the bonds long term (LONG TERM INVESTOR:
        Will enter risky strategy only if expects lower prices => higher future interest rates=>E(r_2 )>f_2)
        dominated by SHORT TERM investor: Investors Require a premium for buying long-term bonds
        
        If short-term investors dominate: E(r_n )<f_n^ (positive liquidity premium) If long-term investors dominate: E(r_n )>f_n^ (negative liquidity premium)
    - - Modified Duration: D*=D/(1+y) -> change in price= -modified D x change in y
      - Duration is just linear approximation -> because we have only small interests therefore its correct to assume the duration as correct
      - Convexity= 1/(P(1+y)^2) * sum of (CF_t / (1+y)^t) (t^2 + t)
      - Higher frequency of coupons -> lower duration (effective coupon p.a. > with higher frequency -> duration decrease in coupon
- - - - To compare different horizonts we express investments as Effective Annual Rate (EAR)
        
        compound rates: is the addition of interest to the amount of money originally invested (principal) => EAR
        
        1+EAR= (1+r(T))^1/T = (1 + T* APR)^1/T
        
        E(r)=∑_s * p(s)×r(s); σ=√(∑_s p(s)×(r(s)-E(r))^2); Sharpe ratio= SR = Risk premium / St.d. of returns = gain / loss
        
        simple rates: previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. => Annual Percentage Rate (APR) => credit cards, car/ student loans
        
        APR= n*r(T) = ((1+EAR)^T - 1) / T
  - - - Decrease in after tax real return= -i t .....tax liabilities are based on nominal income- r_nom (1-t) - i = r_real(1 - t) - i*t
  - - - A > 0 -> Dont like risk (risk averse); A=0 -> risk neutral; A < 0-> risk seeking
      - Indifference curves- set of risk and rewards that provide the same utility to the consumer
    - - y=portion in risky portfolio .... 1-y = portion in risk-free assets
      - Expected return: E(r_c) = r_f + y (E(r_p) - r_f).........o_c=yo_p => y= o_c / o_p => E(r_c)= r_f + o_c * (Risk premium/o_p) ("sharpe ratio")
      - CAPITAL ALLOCATION LINE (CAL)- combination of risk and return investor can choose from -> slope = sharpe ratio
        
        leverage- makes possible to have y>1 by borrowing at a risk free rate
    - - Active: we analyze all stocks individually and, based on this, we choose the optimal allocation
      - A passive strategy- avoids security analysis -> buy a large already well diversified portfolio of stocks (S&P 500 proxy for the market)
      - The Capital Market Line (CML) is a capital allocation line formed from the market portfolio, M, where T-bills are used as the risk-free rate as T-bills are very close to being risk-free.
    - - Firm specific risk (how will the company do) -> can be diversified away
        
        σ_P=√(w_E^2 σ_E^2+(1-w_E^ )^2 σ_D^2+2w_E (1-w_E)σ_E σ_D ρ_ED )
        
        σ_DE=ρ_DE σ_D σ_E
        
        Risk reduction: perfectly correlated (cannot reduce risk) - ρ_ED=1 ..................less than perfectly correlated (potential for risk reduction) - -1<ρ_ED<1.......perfectly negatively correlated (riskless hedge possible) - ρ_ED=-1
      - Market risk (business cycle, inflation, tax laws)
      - Min. variance portfolio- w_e = (o_D^2 - o_ED) / (o_E^2 +o_D^2 - 2o_ED).............w_d = (o_e^2 - o_ED) / (o_E^2 +o_D^2 - 2o_ED)
      - Optímal risky portfolio (max SR)-w_D=((E(r_D )-r_f)σ_E^2-(E(r_E )-r_f)σ_DE^ )/((E(r_D )-r_f)σ_E^2+(E(r_E )-r_f)σ_D^2-(E(r_D)-r_f+E(r_E)-r_f)σ_DE )
- - - - Joint hypothesis problem: all firms have the same risk-to-reward (higher risk higher returns) -> small firms have higher realized returns than expected returns -> either EHM does not hold or we estimate the risk of small firms wrongly
      - value stock: stock traded at levels below its fundementals (book value= what one would get if the company gets liquidated) -> high book-to-market value
      - anomalies: momentum - stocks with recently good performance outperform other stocks
        Volatility- low volatility stocks have higher returns
- - - - If a firm wants to increase share prices: Cut dividends and invest more
        Cut investments and increase dividends (depends on how profitable the new investments are)
        -> New investments will lead to higher share prices only if the investments have positive NPV
      - Free Cash Flow valuation: P0= PV (future dividends per share) = PV (future dividends and repurchases) / Shares outstanding0
        
        Enterprise Value=V0 (current value)= Market Value of Equity + Debt - Cash = PV (Future Free Cash Flows)
        
        Weighted Average Cost of Capital-> because of leverage we need to use WACC to dicount FCF for both equity and debt holders (debt 0 => r_wacc=r_e)
        V0= FCF1 / (1+r_wacc)^1 + ... + FCF_N / (1+r_wacc)^N + V_N / (1+r_wacc)^N
        Terminal value V_N- estimated by assuming constant growth of FCF after year N => V_N= FCF_N+1 / (r_wacc - g_FCF)= FCF_N * (1+g_FCF) / (r_wacc - g_FCF)
        
        Valuation based on comparable firms
        
        Method of comparables- estimate firm value based on a comparable firm with similar expected cash flows (might not exist)
        Valuation multiple- measure value relative to measure of the firm´s scale-> P/E ratio: P/shares_A= P/Shares_A * P/E_B
    - - The Dividend-Discount Model:
        One year: P0=(Div1+P1) / (1+r_E ) represents a zero-NPV investment
        For horizon N: P0= Div1/ (1+r_e)^1 + ....+ DivN / (1+r_E)^N + P_N / (1+r_E)^N
        
        equity cost of capital, r_E, is defined as the expected return of other investments available in the market with equivalent risk to the firm’s shares
        
        r_E=(Div_1+P_1)/P_0 -1=Div_1/P_0 + (P_1-P_0)/P_0
        Divident yield= Div_1/P_0= exp. % divident return
        Capital gain rate= P1 - P0 / P0 = exp. earnings from selling
        
        constant dividend growth: P0 = Div1 / (r_E - g)
        
        Dividends_t = (Earnings_t / Shares Outstanding_t) * Dividend payout rate_t
        
        If the number of shares is constant, the dividends can be increased by: increase earnings, increase dividend payout rate
        
        Things to do with earnings: 1. Pay out dividends 2. Reinvest
        
        change in earnings = New investment Return on new investment
        New investment = Earnings Retention rate = CapEx - Deprec.
        Earnings Growth Rate = Change in Earnings / Earnings = Retention rate Return on New Investment
        g = Retention rate Return on new investments