1

Introduction

A. Caggia – M. ArmaniniFinancial Investment & Pricing

2015-2016

Why are you here ?

Prerequisite: math (NPV, IRR…) statistics (normal distribution, probability theory…),

Goal: gain the basic tools to value (any?) financial assets

Why: professional career in Finance, managing personal investments, become literate in Finance

2

Self assesment1. If I invest 100 today and receive 121 euros in two years time the

compounded interest rate I receive is equal to …2. The Net Present Value of 100 euros that I will be receiving in

three years time calculated at a 10% compounded yearly is… (show calc)

3. When interest rates increase the price of a fixed coupon bond increase/decrease/no change. Why?

4. If interest rates are at 10%, a 10% coupon bond is trading at …5. If interest rates decrease I am better off if I own a 10 year

bond, a 5 year bond or have cash ? Why?6. If the performance of my portfolio in the last 5 years has been

respectively +20%, +10%, -10%,+5%, -25% I am achieving a positive/negative/zero return? Show calc

7. If the price of a share increases by 60% in year 1 and decreases by 50% the following year I am flat/losing/gaining? Show calc

3

What will we be doing?

Look at the world from the investor point of view

What can I invest in? Which is the risk return profile of a single asset?

How should I find the fair price of a financial asset?

How a portfolio behaves?

4

Corporate Finance vs Financial Investmens Different sides of the same coinCorporate finance: identify funding needs and raise capital

Financial Investment: invest in a risk return efficient fashion

In the middle: Investment Banks and Financial Engeneering

5

Logistics Our mails are:

marmanini@liuc.itacaggia@liuc.it

Read material before coming to class

What to read/study Exam Behaviour/contract

6

7

Investments & Financial Assets

Essential nature of investmentReduced current consumptionPlanned later consumption or investments

Real AssetsAssets used to produce goods and services

Financial AssetsClaims on real assets

8

Consumption Timing

Allocation of Risk

Separation of Ownership

Role of Financial Assets and Markets in

the Economy

Financial System Clients and Their Needs

Household SectorPrimary need: invest funds

Business SectorPrimary need: raise funds

Government SectorPrimary need: raise funds

9

10

Financial Assets

What can I invest in?

11

Financial Assets or Securities

DebtMoney market instruments Bonds

Equities Forex Commodities Derivatives

Debt – Money Market instruments

Treasury Bills (ex. BOT) Certificates of Deposit Commercial Paper Bank Loan Euribors Repurchase Agreement (repos) and Reverse RP

Central Bank Funds

12

Debt – Bonds

Treasury Bond (ex. BTP)

Agency and Supranational Issue

Asset Backed Security

Corporate Bond

13

Common and Preferred Stocks

Common StockResidual claimLimited liabilities

Preferred StockFixed dividend ratePriority over common

14

Commodities Energy

Oil, natural gas, carbon, electricity, emissions

MetalsBase Metals: copper, nickel, aluminium, zinc

Precious Metals: gold, silver, platinum Agriculture

Soy beans, wheat, rice

15

Derivatives Securities

OptionsBasic positions: call (buy), put (sell)

Terms: exercise price, expiration date, assets

FuturesBasic positions: long (buy), short (sell)

Terms: delivery date, assets

16

Other

Any mixture of the above mentioned: convertible bonds, warrants, rights, hibrids, hedge funds …

17

What do they have in common ? Cash Flow Streams

DeterministicUncertain (in amount and/or timing)

Need to compare them to efficiently allocate resources (pricing)

18

How securities are traded Equity Bonds Money Market instruments FX Commodities Futures and Options Funds

19

Financial Markets Data

20

21

Portfolio Management

Definitions

22

Portfolio = is a set of financial instruments

Asset Allocation = is the decision by the investor of the types and amounts of assets to assign to a portfolio

Portfolio Management = is the activity of constructing and following the evolution of a portfolio during its lifetime, by balancing risk and reward

Portfolio Composition

23

EquitiesBondsCurrencyCommoditiesIndex

Returns

24

Single Asset Return (R) = is the percentage increase (or decrease) in the value of the asset during a period of time (e.g. one week)

First a quick refresh

X,Y = two random variable expected value, variance, covariance and correlation

In our case the random variables are the returns

201225

Expected Value, Mean, Average

201226

Returns

27

Portfolio Return (Rp) = is the percentage increase (or decrease) in the value of the portfolio during a period of time (e.g. one week)

Two assets:

N assets:

Variance

201228

Variance of Sum

Var(x + y) = var(x) + var(y) + 2 cov(x,y)

201229

Covariance

201230

Correlation Coefficient

• A scaled measure of how much two variables move toghether

• -1 ≤ r ≤ 1 rx,y = cov(x,y) / (sxsy)

Massimo Armanini

201231

Portfolio Selection (1952) Harry Markowitz (1927) in 1952 (age 25) published an article that changed the way we look at risk.

Nobel price 1990 …

201232

A Portfolio of a Risky and a Riskless Asset Put x euro in risky asset 1, (1-x) euro in the riskless asset earning a sure return rf

Portfolio expected value r = xr1 + (1 – x)rf

Portfolio variance = x2 var(r1)

2012

Std Dev

rf

Capital Market Line

201234

201235

201236

Put x1 euro in risky asset 1 and (1- x1) euro in risky asset 2 .

Portfolio expected value r=x1r1+(1-x1)r2

Portfolio variance = X2

1var(return1 )+ (1− x1 )2 var(return2 )+

2x1 (1−x1 )cov(return1,return2 )

201237

Efficient Portfolio Frontier Stocks and Bonds

201238

Portfolio expected returns as a function of weights

201239

If wd=1.5 and we = -0.5 (short equity long fund bonds) Expected return= 5.5%%

Portfolio Std Dev as a function of weights

201240

With R=.30, std first falls for diversification benefit, then it grows because equity weights more and diversification benefits are decreasing

Portfolio expected returns as a function of std dev

201241

R=1 perfectly correlated, no diversification benefitsR=-1 perfectly negatively correlated Max diversification benefit could reach 9,875% with zero std dev. Weights wd=0,625, we=0,275R=0 no correlation min portfolio std dev 10,29% expected return 9,32%R=0,30 exp return 8,9% std dev 11,44

Important to notice There are portfolios where the std dev is lower than either of the two components (e.g. min variance portfolio)

Potential benefits from diversification are greater if correlation is less then perfectly positive

Decisions on where to position on the efficient frontier is risk aversion linked

201242

Portfolio Variance, Three Risky Assets

• Portfolio variance =x2

1 var(return1) + x22 var (return2) + x2

3var(return3)

+ 2x1x2 cov(return1,return2) + 2x1x3 cov(return1,return3) + 2x2x3 cov(return2,return3)

201243

Efficient Portfolio with and without Oil

201244

Sharpe Ratio for a Portfolio

201245

Ref: Yale University Publications Investment and Portfolio Management, Bodie Kane and Marcus Robert Shiller, Financial Markets

201246