LECTURE 1 : THE BASICS

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) (1R) / P1g
• (1Rr) ? W1r/W0r (1 R)/(1p)
• Rr ? DW1r/W0r (R p)/(1p) ? R p
• Continuously compounded returns
• ln(W1r/W0r) ? Rcr ln(1R) 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

• Ht1 (Pt1Pt)/Pt Dt1/Pt
• 1Ht1 (Pt1 Dt1)/Pt
• Y A(1Ht1(1))(1Ht2(1)) (1Htn(1))
• Continuously compounded returns
• One period ht1 ln(Pt1/Pt) pt1 pt
• N periods htn ptn - pt ht ht1 htn
• 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 gt P (price of stock) or V gt 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 SP500), 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 / (1r)2 1,210/(1.10)2
• Hence DPV of 1,210 is 1,000
• Discount factor d2 1/(1r)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/(1r) V2/(1r)2
• d1 V1 d2 V2
• d discount factor lt 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/(1r)i
• Formula for sum of geometric progression
• DPV CAn,r where An,r (1/r) 1- 1/(1r)n
• DPV C/r for n ? 8

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 gt 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 gt KC or NPV gt 0
• IRR gt 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