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Foundations of Finance Notes Sheet

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MULTIPLE PAYMENT | |

ANNUITIES | PERPETUITIES |

EFFECTIVE ANNUAL RATE Periodic Compounding | Continuous Compounding | M = times compounded in the year, APR = Annual Percentage Rate (annual quoted rate) |

HOLDING PERIOD RETURN Buy investment at price V(0), reinvest all cash flows until period T, sell investment and reinvested cash flow for V(T). V(T) = ending prince + cash dividend |

INTERNAL RATE OF RETURN (calculator input) Initial Capital Contribution | 1st period return | 2nd period return | 3rd period return | | STATSTICSCorrelation | Standard Deviation, where p = probabilityVariance | Covariance | | | If two securities are perfectly negatively correlated (i.e.), complete the squarei.e. if .and , then , and |

MEAN VARIANCE UTILITY

where A is risk aversion ([risk neutral] 0 ≤ A ≤ 1 [risk averse])

SHARPE RATIO CAPITAL ALLOCATION LINE , where = w

SINGLE INDEX MODEL Idiosyncratic Risk Idiosyncratic Risk

Systemic Risk Systemic Risk

SECURITY MARKETS LINE , where
This can also be used to find the discount rate as E[Ri]

Security I’s alpha is:

________________________________________________________________________________
GORDON’S GROWTH MODEL
Price-Earnings Ratio Sensitivity of Price-Earnings Ratio w.r.t. b Price-Dividend Ratio

R = required returns, g = expected growth, b = 1 – D0/E0 = plowback

Return on Equity = g/b
________________________________________________________________________________

FIXED INCOME Principal Repayment Coupon Receipt | FORWARDS |
DURATION
, where , and , and P = price. Perpetuity duration =
Duration of zero-coupon bond = time to maturity
IMMUNIZATION
Dassets = Dliabilities , find as weightings of each security if either is expressed as multiple fixed income securities.

OPTIONS
PUT-CALL PARITY , where P0 = put price, and PV0(Div) = present value of dividend payments. BLACK-SCHOLESwhere, and | Determinants of Option Values If higher… | Call (C0) | Put(P0) | Stock price today (S0) | + | | - | Exercise Price (X) | - | | + | Volatility of Stock (σ) | + | | + | Interest Rate (r) | + | | - | Time to Expiration (T) | + | | Depends on interest rate | | | Buy Δ shares for each call option written(latter is hedge ratio for futures) | FUTURESHedging with futures: Pricing Futures: | Where,r = interest rates = storage costl = leasing benefitT= years |
HEDGE RATIO

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