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LECTURE 1 : THE BASICS

LECTURE 1 : THE BASICS. (Asset Pricing and Portfolio Theory). Contents. Prices, returns, HPR Nominal and real variables Basic concepts : compounding, discounting, NPV, IRR Key questions in finance Investment appraisal Valuating a firm. Calculating Rates of Return.

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LECTURE 1 : THE BASICS

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  1. LECTURE 1 :THE BASICS (Asset Pricing and Portfolio Theory)

  2. Contents • Prices, returns, HPR • Nominal and real variables • Basic concepts : compounding, discounting, NPV, IRR • Key questions in finance • Investment appraisal • Valuating a firm

  3. Calculating Rates of Return • Financial data is usually provided in forms of prices (i.e. bond price, share price, FX, stock price index, etc.) • Financial analysis is usually conducted on rate of return • Statistical issues (spurious regression results can occur) • Easier to compare (more transparent)

  4. Prices  Rate of Return • Arithmetic rate of return Rt = (Pt - Pt-1)/Pt-1 • Continuous compounded rate of return Rt = ln(Pt/Pt-1) • get similar results, especially for small price changes • However, geometric rate of return preferred • more economic meaningful (no negative prices) • symmetric (important for FX)

  5. Exercise : Prices  Rate of Return • Assume 3 period horizon. Let • P0 = 100 • P1 = 110 • P2 = 100 • Then : • Geometric : R1 = ln(110/100) = ??? and R2 = ln(100/110) = ??? • Arithmetic : R1 = (110-100)/100 = ??? and R2 = (100-110)/110 = ???

  6. Nominal and Real Returns • W1r W1/P1g = [(W0rP0g) (1+R)] / P1g • (1+Rr)  W1r/W0r = (1 + R)/(1+p) • Rr  DW1r/W0r = (R – p)/(1+p)  R – p • Continuously compounded returns ln(W1r/W0r)  Rcr = ln(1+R) – ln(P1g/P0g) = Rc - pc

  7. Foreign Investment • W1 = W0(1 + RUS) S1 / S0 • R (UK  US)  W1/W0 – 1 = RUS + DS1/S0 + RUS(DS1/S0)  RUS + RFX • Nominal returns (UK residents) = local currency (US) returns + appreciation of USD • Continuously compounded returns Rc (UK  US) = ln(W1/W0) = RcUS + Ds

  8. Summary : Risk Free Rate, Nominal vs Real Returns • Risk Free Asset • Risk free asset = T-bill or bank deposit • Fisher equation : Nominal risk free return = real return + expected inflation Real return : rewards for ‘waiting’ (e.g 3% - fairly constant) Indexed bonds earn a known real return (approx. equal to the long run growth rate of real GDP). • Nominal Risky Return (e.g. equity) Nominal “risky” return = risk free rate + risk premium risk premium = “market risk” + liquidity risk + default risk

  9. FTSE All Share Index : (Nominal) Stock Price

  10. FTSE All Share Index : (Nominal) Returns

  11. FTSE All Share Index : (Real) Stock Price

  12. FTSE All Share Index : (Real) Returns

  13. Holding Period Return (Yield) : Stocks • Ht+1 = (Pt+1–Pt)/Pt + Dt+1/Pt • 1+Ht+1 = (Pt+1 + Dt+1)/Pt • Y = A(1+Ht+1(1))(1+Ht+2(1)) … (1+Ht+n(1)) • Continuously compounded returns • One period ht+1 = ln(Pt+1/Pt) = pt+1 – pt • N periods ht+n = pt+n - pt = ht + ht+1 + … + ht+n • where pt = ln(Pt)

  14. Finance : What are the key Questions ?

  15. ‘Big Questions’ : Valuation • How do we decide on whether … • … to undertake a new (physical) investment project ? • ... to buy a potential ’takeover target’ ? • … to buy stocks, bonds and other financial instruments (including foreign assets) ? • To determine the above we need to calculate the ‘correct’ or ‘fair’ value V of the future cash flows from these ‘assets’. If V > P (price of stock) or V > capital cost of project then purchase ‘asset’.

  16. ‘Big Questions’ : Risk • How do we take account of the ‘riskiness of the future cash flows when determining the fair value of these assets (e.g. stocks, investment project) ? • A. : Use Discounted Present Value Model (DPV) where the discount rate should reflect the riskiness of the future cash flows from the asset  CAPM

  17. ‘Big Questions’ • Portfolio Theory : • Can we combine several assets in order to reduce risk while still maintaining some ‘return’ ?  Portfolio theory, international diversification • Hedging : • Can we combine several assets in order to reduce risk to (near) zero ?  hedging with derivatives • Speculation : • Can ‘stock pickers’ ‘beat the market’ return (i.e. index tracker on S&P500), over a run of bets, after correcting for risk and transaction costs ?

  18. Compounding, Discounting, NPV, IRR

  19. Time Value of Money : Cash Flows Project 1 Project 2 Project 3 Time

  20. Example : PV, FV, NPV, IRR Question : How much money must I invest in a comparable investment of similar risk to duplicate exactly the cash flows of this investments ? Case : You can invest in a company and your investment (today) of £ 100,000 will be worth (with certainty) £ 160,000 one year from today. Similar investments earn 20% p.a. !

  21. Example : PV, FV, NPV, IRR (Cont.) + 160,000 r = 20% (or 0.2) Time 0 Time 1 -100,000

  22. Compounding • Example : A0 is the value today (say $1,000) r is the interest rate (say 10% or 0.1) Value of $1,000 today (t = 0) in 1 year : • TV1 = (1.10) $1,000 = $1,100 Value of $1,000 today (t = 0) in 2 years : • TV2 = (1.10) $1,100 = (1.10)2 $1,000 = $ 1,210. Breakdown of Future Value $ 100 = 1st years (interest) payments $ 100 = 2nd year (interest) payments $ 10 = 2nd year interest payments on $100 1st year (interest) payments

  23. Discounting • How much is $1,210 payable in 2 years worth today ? • Suppose discount rate is 10% for the next 2 years. • DPV = V2 / (1+r)2 = $1,210/(1.10)2 • Hence DPV of $1,210 is $1,000 • Discount factor d2 = 1/(1+r)2

  24. Compounding Frequencies Interest payment on a £10,000 loan (r = 6% p.a.) • Simple interest £ 10,000 (1 + 0.06) = £ 10,600 • Half yearly compounding £ 10,000 (1 + 0.06/2)2 = £ 10,609 • Quarterly compounding £ 10,000 (1 + 0.06/4)4 = £ 10,614 • Monthly compounding £ 10,000 (1 + 0.06/12)12 = £ 10,617 • Daily compounding £ 10,000 (1 + 0.06/365)365 = £ 10,618.31 • Continuous compounding £ 10,000 e0.06 = £ 10,618.37

  25. Effective Annual Rate (1 + Re) = (1 + R/m)m

  26. Simple Rates – Continuous Compounded Rates AeRc(n) = A(1 + R/m)mn Rc = m ln(1 + R/m) R = m(eRc/m – 1)

  27. FV, Compounding : Summary • Single payment FVn = $A(1 + R)n FVnm = $A(1 + R/m)mn FVnc = $A eRc(n)

  28. Discounted Present Value (DPV) • What is the value today of a stream of payments (assuming constant discount factor and non-risky receipts) ? DPV = V1/(1+r) + V2/(1+r)2 + … = d1 V1 + d2 V2 + … d = ‘discount factor’ < 1 Discounting converts all future cash flows on to a common basis (so they can then be ‘added up’ and compared).

  29. Annuity • Future payments are constant in each year : FVi = $C • First payment is at the end of the first year • Ordinary annuity DPV = C S 1/(1+r)i • Formula for sum of geometric progression DPV = CAn,r where An,r = (1/r) [1- 1/(1+r)n] DPV = C/r for n  ∞

  30. Investment Appraisal (NPV and DPV) • Consider the following investment • Capital Cost : Cost = $2,000 (at time t= 0) • Cashflows : Year 1 : V1 = $1,100 Year 2 : V2 = $1,210 • Net Present Value (NPV) is defined as the discounted present value less the capital costs. NPV = DPV - Cost • Investment Rule : If NPV > 0 then invest in the project.

  31. Internal Rate of Return (IRR) • Alternative way (to DPV) of evaluating investment projects • Compares expected cash flows (CF) and capital costs (KC) • Example : KC = - $ 2,000 (t = 0) CF1 = $ 1,100 (t = 1) CF2 = $ 1,210 (t = 2) NPV (or DPV) = -$2,000 + ($ 1,100)/(1 + r)1 + ($ 1,210)/(1 + r)2 IRR : $ 2,000 = ($ 1,100)/(1 + y)1 + ($ 1,210)/(1 + y)2

  32. Graphical Presentation : NPV and the Discount rate NPV Internal rate of return 0 8% 10% 12% Discount (loan) rate

  33. Investment Decision • Invest in the project if : DPV > KC or NPV > 0 IRR > r if DPV = KC or if IRR is just equal the opportunity cost of the fund, then investment project will just pay back the principal and interest on loan. • If DPV = KC  IRR = r

  34. Summary of NPV and IRR • NPV and IRR give identical decisions for independent projects with ‘normal cash flows’ • For cash flows which change sign more than once, the IRR gives multiple solutions and cannot be used  use NPV • For mutually exclusive projects use the NPV criterion

  35. References • Cuthbertson, K. and Nitzsche, D. (2004) ‘Quantitative Financial Economics’, Chapter 1 • Cuthbertson, K. and Nitzsche, D. (2001) ‘Investments : Spot and Derivatives Markets’, Chapter 3 and 11

  36. END OF LECTURE

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