FIN301 • Course Hub Fall 2026

1) Big idea: return vs. risk

• Return = reward for investing (what you expect/earn).
• Risk = uncertainty of returns (how much actual return can differ from expected return).
• In finance, we usually measure risk with variance or standard deviation (SD).
• Higher expected return usually requires higher risk.

2) One-stock expected return (probability approach)

• Expected return: E(R) = Σ [ pi × Ri ]
• Multiply each possible return by its probability, then add them up.
• Probabilities should sum to 1.00 (or 100%).

3) One-stock risk (variance and standard deviation)

• Variance: σ² = Σ [ pi × (Ri − E(R))² ]
• Standard deviation: σ = √σ²
• SD is easier to interpret because it is in the same unit as returns (e.g., %).
• Larger SD = more spread/volatility = more risk.

4) Two-stock portfolio: expected return

• Portfolio expected return is a weighted average:
• E(Rp) = wAE(RA) + wBE(RB)
• Weights must add to 1: wA + wB = 1
• If you invest 60% in A and 40% in B, then weights are 0.60 and 0.40.

5) Two-stock portfolio risk depends on correlation

• Portfolio risk is not just the weighted average of individual SDs (except in special cases).
• It also depends on how the two stocks move together: correlation (ρ).
• Key rule: lower correlation → more diversification benefit.
• Correlation range: -1 ≤ ρ ≤ +1

6) Diversification intuition (Apple + Walmart example)

• Suppose you already own Apple and want to add another stock.
• If Apple and Walmart have a relatively low correlation (assume about 0.11), combining them can reduce portfolio volatility more than combining Apple with another stock that moves very similarly to Apple.
• Why Walmart? Different business model / demand drivers can help reduce co-movement.
• That does not guarantee higher return, but it can improve the portfolio’s risk-return tradeoff.

7) Systematic vs. unsystematic risk

• Unsystematic risk (firm-specific risk): company events (lawsuits, management issues, product failures). This risk can be reduced by diversification.
• Systematic risk (market risk): economy-wide risk (interest rates, recessions, inflation, market shocks). This risk cannot be diversified away.
• CAPM focuses on systematic risk.

8) Beta (β): the CAPM risk measure

• Beta measures systematic (market) risk, not total risk.
• β = 1.0: same market sensitivity as the market.
• β > 1.0: more sensitive than the market (higher systematic risk).
• β < 1.0: less sensitive than the market (lower systematic risk).
• β = 0: no market sensitivity (theoretical benchmark).
• β < 0: moves opposite the market (rare, but possible for hedging-type assets).

9) CAPM formula (required return)

• CAPM: R̂ = Rf + β ( Rm − Rf )
• Rf = risk-free rate
• Rm = expected market return
• (Rm − Rf) = market risk premium (MRP)
• R̂ = required return (or cost of equity estimate in many applications)

10) Security Market Line (SML)

• The SML is the graph of CAPM required return versus beta.
• Y-axis: required return
• X-axis: beta
• Intercept: Rf
• Slope: (Rm − Rf) (market risk premium)

11) Using the Chapter 6 calculators (JUFinance)

• One-Stock Return/Risk Calculator: use for expected return, variance, and SD of a single stock.
• Two-Stock Portfolio Calculator: test different weights and correlation assumptions to see diversification effects.
• CAPM Calculator: compute required return using risk-free rate, beta, and market return (or market risk premium).

12) Common mistakes (watch these on quizzes/exams)

• Using % values incorrectly (e.g., entering 12 instead of 0.12 in formulas/calculators).
• Confusing expected return with standard deviation.
• Assuming portfolio SD is a simple weighted average.
• Forgetting correlation/covariance in two-stock portfolio risk.
• Saying diversification removes market risk (it removes mostly firm-specific risk).
• Calling beta “total risk” (in CAPM, beta = systematic risk).
• Mixing up SML intercept (risk-free rate) and SML slope (market risk premium).

1) Basic bond ideas

• Par value: usually $1,000
• Coupon rate: stated annual interest rate
• Coupon payment: coupon rate × par value
• Maturity: when par value is repaid
• Bond price: present value of all future cash flows

2) Bond cash flows

• Coupon bond: periodic coupon payments + par value at maturity
• Zero-coupon bond: no periodic coupons; only par value at maturity
• Investor cash flows = coupons each period and final repayment of principal

3) Price and yield move in opposite directions

• If YTM goes up, bond price goes down
• If YTM goes down, bond price goes up
• Longer maturity bonds usually have greater price sensitivity

4) Key formulas

• Current Yield: annual coupon / bond price
• Annual coupon bond price: =ABS(PV(yield, maturity, coupon, 1000))
• Semi-annual bond price: =ABS(PV(yield/2, maturity*2, coupon/2, 1000))
• Annual YTM: =RATE(maturity, coupon, -price, 1000)
• Semi-annual YTM: =RATE(maturity*2, coupon/2, -price, 1000)*2

5) Premium, discount, and par bonds

• Premium bond: price > par when coupon rate > YTM
• Discount bond: price < par when coupon rate < YTM
• Par bond: price = par when coupon rate = YTM

6) What to practice

• Price a coupon bond from a given YTM
• Solve YTM from a given market price
• Compute current yield
• Compare annual vs. semi-annual bonds
• Use the bond calculator and FINRA bond data together

1) Big idea: what is stock valuation?

• A stock is worth the present value of future cash flows to shareholders.
• For many firms, those cash flows are modeled as future dividends.
• Stock value depends mainly on: expected dividends, growth, and the required return.

2) General dividend valuation model

• General form: P0 = D1/(1+r) + D2/(1+r)2 + D3/(1+r)3 + ...
• P₀ = stock price today
• D_t = dividend expected at time t
• r = required return on equity

3) Zero-growth stock

• If dividends stay constant forever, then the stock acts like a perpetuity.
• Formula: P0 = D / r
• This is often used for preferred stock when the dividend is fixed.

4) Constant-growth (Gordon) model

• If dividends grow at a constant rate g, then:
• Formula: P0 = D1 / (r - g)
• Next dividend: D1 = D0(1+g)
• Required condition: r > g

5) What makes stock price go up or down?

• Price goes up when expected dividends increase.
• Price goes up when expected growth g increases.
• Price goes down when required return r increases.
• More risk usually means a higher required return, which lowers valuation.

6) Required return from the Gordon model

• Rearrange the constant-growth model:
• Required return: r = D1/P0 + g
• This says total expected return = dividend yield + growth rate.

7) Preferred stock valuation

• Preferred stock usually pays a fixed dividend.
• Formula: Pp = Dp / rp
• It is valued like a perpetuity.

8) Non-constant growth idea

• Some firms grow fast first, then settle into stable growth later.
• In that case, value the early dividends one by one, then use the Gordon model for the stable-growth stage.
• Two-stage idea: discount the first stage separately, then add the discounted terminal value.

9) Quick intuition

10) Common mistakes

• Using D₀ instead of D₁ in the Gordon model.
• Forgetting to grow the dividend first: D1 = D0(1+g).
• Using the model when r ≤ g.
• Mixing up dividend yield and growth rate.
• Forgetting that a higher required return lowers present value.