1 Introduction A. Caggia – M. Armanini Financial Investment & Pricing 2015-2016.
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Transcript of 1 Introduction A. Caggia – M. Armanini Financial Investment & Pricing 2015-2016.
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
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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
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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?
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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
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Logistics Our mails are:
[email protected]@liuc.it
Read material before coming to class
What to read/study Exam Behaviour/contract
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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
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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
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Financial Assets
What can I invest in?
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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
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Debt – Bonds
Treasury Bond (ex. BTP)
Agency and Supranational Issue
Asset Backed Security
Corporate Bond
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Common and Preferred Stocks
Common StockResidual claimLimited liabilities
Preferred StockFixed dividend ratePriority over common
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Commodities Energy
Oil, natural gas, carbon, electricity, emissions
MetalsBase Metals: copper, nickel, aluminium, zinc
Precious Metals: gold, silver, platinum Agriculture
Soy beans, wheat, rice
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Derivatives Securities
OptionsBasic positions: call (buy), put (sell)
Terms: exercise price, expiration date, assets
FuturesBasic positions: long (buy), short (sell)
Terms: delivery date, assets
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Other
Any mixture of the above mentioned: convertible bonds, warrants, rights, hibrids, hedge funds …
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What do they have in common ? Cash Flow Streams
DeterministicUncertain (in amount and/or timing)
Need to compare them to efficiently allocate resources (pricing)
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How securities are traded Equity Bonds Money Market instruments FX Commodities Futures and Options Funds
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Financial Markets Data
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Portfolio Management
Definitions
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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
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EquitiesBondsCurrencyCommoditiesIndex
Returns
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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
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Expected Value, Mean, Average
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Returns
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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
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Variance of Sum
Var(x + y) = var(x) + var(y) + 2 cov(x,y)
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Covariance
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Correlation Coefficient
• A scaled measure of how much two variables move toghether
• -1 ≤ r ≤ 1 rx,y = cov(x,y) / (sxsy)
Massimo Armanini
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Portfolio Selection (1952) Harry Markowitz (1927) in 1952 (age 25) published an article that changed the way we look at risk.
Nobel price 1990 …
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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
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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 )
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Efficient Portfolio Frontier Stocks and Bonds
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Portfolio expected returns as a function of weights
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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
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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
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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
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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)
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Efficient Portfolio with and without Oil
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Sharpe Ratio for a Portfolio
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Ref: Yale University Publications Investment and Portfolio Management, Bodie Kane and Marcus Robert Shiller, Financial Markets
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