Lecture 1 basics - Peter Corvi taught PDF

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Peter Corvi taught...

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Professor Peter Corvi IB266 Fundamentals of Finance

Lecture 1

0. Basics Key Readings

Hillier, Ross et al. 9.1-9.6 Bodie et al. 5.4-5.5, 18.2

Introduction •

IB235 Finance 1 is mainly concerned with techniques for valuing financial assets – the same techniques will be applied in IB236 Finance 2 to value real assets used in capital projects

•

Examples of financial assets include equities, bonds and derivatives, and we will learn in this module how to value all three

•

In general, to calculate the fair value today of an asset, we need – to forecast the cash flows (e.g. dividends on shares, coupon payments on bonds) that the asset is expected to pay out in the future – a mechanism for expressing those expected future cash flows in so-called present-value terms 1

Risk •

We also need to recognise that assets in the real world are risky – this means that the size and timing of the future cash flows are uncertain

•

So we also have to have some means of modelling (and measuring) risk

•

Statistics provides some of the answers – best forecast of a future cash flow is the expected value (in the sense of the mean of the distribution of possible values) of that future cash flow – risk is measured by the variance (or equivalently its square root, the standard deviation) of the distribution of possible values for that future cash flow

•

How banks calculate compound interest provides a clue as to how to calculate present values – run compound interest calculation in reverse gear

Certain vs. Uncertain • •

•

•

We will start by assuming a world of certainty and learn how to discount future cash flows that are known today with certainty back to the present day We will then introduce risk – risk will be incorporated in our models by assuming that any one of a number of states are possible in the future We will assume that the payoff in each of these possible future states is known today with certainty – what we don’t know today is which of these states will occur at that point in the future – we will also assume that we know the probabilities that each of these states will occur What we will need to be able to calculate, then, are – the expected (in the sense of the probability-weighted average) future cash flow – the variance (and hence standard deviation) of possible values for that future cash flow

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Different Outcomes • Uncertainty about future payoff Pt+1 is modelled by assuming there are a number of possible states 1, 2, … N next period with probabilities p1, p2, … pN time t

time t+1 state 1

P(1) t1

p1

P(2)1 t

p2 . .

Pt

state 2

. .

pN

P (N1 ) t

state N

• Probabilities sum to 1: π1 π2 ...  π N  1 • Expected future payoff E[Pt+1] is given by: E[ P ]  π  P(1)  π  P(2) ...  π Ν  P( N ) t 1

1 t 1

2 t 1

t 1

• Variance var[Pt+1] of future payoffs: 

2

(1)



(2)

2



(N )

2

 E[P ] var[Pt 1 ]  π1  P  E[P ]  π2  P  E[P ]  ...  π Ν  P t 1  t  1   t 1  t 1  t 1 t 1    

Rates of Return •

Often, it will be more convenient to work in terms of returns rather than payoffs or cash flows

•

If we pay Pt today for a share of stock, hold on to it for one period in order to receive the dividend D t+1 that it pays at the end of that period, and then sell the share for P t+1 , our one-period rate of return Rt equals: Rt 

(Pt 1 Pt )  Dt1 Pt



Pt 1 Dt 1  Pt  (1 Rt )

•

There are two components to this rate of return – capital gain = (P t+1 -Pt)/Pt – dividend yield = Dt+1 /Pt

• •

This method of calculating rates of return is known as discrete compounding Continuously-compounded rates of return are calculated as follows (no dividends): P    Rt  ln  t 1   Pt  





R Pt 1  Pt e t

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Example • Three equally-likely scenarios next period Scenarios: – “recession”, “normal”, “growth” • Two investment prospects – shares in car manufacturers, gold

• Sample calculations:

1. “Recession” 2. “Normal”

Rate of Return R Cars Gold -8% 20% 5% 3%

3. “Growth” 18% -20% Expected return 5% 1% Variance of returns 112.7%% 268.7%% Standard deviation 10.6% 16.4% [= variance]

E[ Rcars]  1 ( 8%)  1 (5%)  1 (18%)  5% 3 3 3 var[ Rcars]  1( 8% 5%) 2  1(5% 5%) 2  1 (18%  5%) 2 3 3 3  112.7%%

Summary •

We need to be able to value assets whose future payoffs are not known today with certainty

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Two key issues – how do the future cash flows that the asset pays impact the value of the asset today? – how do we account for fact that these future cash flows are not known today with certainty?

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The first issue requires us to adjust the future cash flows for the time value of money – this process of discounting future cash flows is the reverse of compounding and requires us to know (or estimate) the rate of return

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The second issue requires us to – determine the expected value of the distribution of possible values for each future cash flow – adjust the rate of return that we use to discount these expected future cash flows for the level of risk associated with those cash flows

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Risk is measured by variance (or standard deviation) of distribution of possible future cash flows

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