Finance for Managers Midterm Notes PDF

MIDTERM NOTES Lecture 1 - Firm Objectives & Time Value of Money Business Corporation - A separate legal entity, Separation of ownership and control – (shareholders own the company, and managers run it), Unlimited life, Easy transfer of ownership, Easy to raise capital. Limited...

MIDTERM NOTES Lecture 1 - Firm Objectives & Time Value of Money Business Corporation - A separate legal entity, Separation of ownership and control – (shareholders own the company, and managers run it), Unlimited life, Easy transfer of ownership, Easy to raise capital. Limited liability The Firm Overriding Objective - Clear decisions require clear objectives. Shareholders are the owners of firms. In competitive market economies, it is assumed that business corporations exist for one overriding objective: 1) to benefit their owners (shareholders), and – to 2) strive to maximise that benefit. = the primary objective is to maximise shareholder wealth Wealth Maximisation - Wealth is the market value (current market price) of ordinary shares, as these reflect the future returns shareholders will expect to receive, taking into account the level of risk. Maximise shareholder wealth by accepting all projects with positive net present values, as this will maximise the market share price. Maximising s/h wealth not same as max profit The Role of Accounting Profit - Accounting profit is a reporting device, not a decision-making device. Profit = past vs Wealth, worth and value = future. Financial decisions are evaluated in terms of their cash flow impact. But profit cannot be ignored: 1) A major criterion by which investors judge a company’s success. 2) Retained profit form a maximum barrier to an annual dividend payment. 3) In the longer run, good cash flows will result in good reported profits Shareholder vs. Stakeholder View? Argue to adopt stakeholder view - broader social and economic view - Studies show that corporations with good business ethics and good corporate governance generally generate higher stock returns BUT - maximising shareholder wealth is the overriding objective - does not mean overlooking other stakeholders Agency Relationships - Agency relationships occur when one party, the principal, employs another party, the agent, to perform a task on their behalf eg. Managers agents of shareholders (most important) - conflicts of interest often exists The Agency Problem (costs) - Shareholders are reliant upon the management to pursue the objectives set for them. Although shareholders can intervene via resolutions at general meeting, the managers are usually left alone day-to-day. Management can maximise their own wealth rather than shareholders. Losses in value from agency problems – or costs incurred to mitigate the problems = agency costs. Agency costs: monitoring expenditures by the principal + bonding expenditures by the agent + residual loss. How to Potentially Fix The Problem? 1) Managerial reward schemes (e.g., executive share option scheme) Managerial compensation can be used to align management and shareholder interests. The incentive need to be structured carefully to make sure that they achieve their intended goal eg. with share price. 2) Corporate Governance Codes: Non-executive directors, Executive directors, Annual General Meeting. 3) Takeovers The threat of a takeover may result in better management. 4) Information requirements Greater presentation requirements for corporations TVM - need to understand so can make decisions to max s/h wealth. Money has a time value because money received today is worth more than the same amount received in the future. £100 today are worth more than £100 in the future. This is for three reasons: 1) Potential for earning interest 2) Impact of inflation 3) Effect of risk Cannot compare cash flows from different time periods straight up - need to either compound (bring PV→FV) or discount (FV→PV) 2 Types of Cash Flows: 1) A conventional cash flow for a project is typically structured as an initial outlay or outflow, followed by a number of inflows over a period of time. 2) Non-conventional cash flows – cash flows that change signs more than once A lump sum is a single flow; for example, a £100 inflow in year 2 Annuity - a series of equal payments or receipts that occur at evenly spaced intervals. Eg. rental payment, regular deposits Ordinary (Standard) Annuity - The payment or receipt occurs at the end of each period. – Example: interest payments on debt and mortgages. Annuity Due - The payment or receipt occurs at the beginning of each period. – Example: leasing arrangements. Delayed Annuity - An annuity with the first payment or receipt starting after year 1. – Example: an annuity with the first payment in four years from now. Growing Annuity - The payment or receipt increases each period at a constant percentage (g). Perpetuity: an annuity that continues indefinitely (i.e. a constant stream of identical cash flows with no end). Ordinary (Standard) Perpetuity - A regular perpetual stream of payments starting one period from now. Delayed Perpetuity - A perpetuity with the first payment starting after year 1.Growing Perpetuity - where the annual payment increases each year at a constant percentage (g). Simple Interest - the amount paid on the original principal (or initial investment) only VS Compound Interest - interest is also paid on the interest already earned = gives higher returns The more frequent the compounding the greater the return = continuous compounding gives the highest return Stated Annual Interest Rate is the rate expressed as a per-year percentage, and that does not account for compounding that occurs throughout the year. VS The Effective Annual Rate (EAR) does account for intra-year compounding that can occur on a daily, monthly or quarterly basis - allows you to compare interest rates across different investments/borrowings. Calculating Cash Payments Using Annuities: 1) A loan = know the present value (how much to borrow) and the interest rate, but you do not know how much you need to repay each year. 2) Savings = know the future value (how much you want to save) and the interest rate, but you do not know how much you need to save each year.  Week 2 - Investment Appraisal Techniques Interest rate = exchange rate of money between points in time - also called - Discount rate when moving future values back to the present OR Rate of return when looking at an investment from the lender’s point of view OR Cost of capital from the borrower’s perspective (e.g., cost of equity, cost of debt, weighted average cost of capital (WACC). Three components of Interest Rate: 1) Pure time preference (PTP) - Price of time (reward for giving up consumption today) 2) Risk premium (RP)- Additional layer from perspective of riskiness. Risk/Return trade-off 3) Inflation premium (IP) - Compensation needed to offset the devaluation of money. Additional layer from perspective of inflation. Risk free interest rate = PTP Real rate of interest = PTP + RP Nominal (money) rate of interest = PTP + RP + IP The Fisher Formula - shows relationship between real (actual) IR and nominal IR under the impact of inflation Risk/Return Trade-off - expected return on Y and risk on X. For a given level of expected return , investor chooses the investment with lowest risk. For a given level of risk, investor chooses the investment with the highest level of expected return The Investment Trade-Off. The financial manager of a firm, has to decide whether or not to invest in a proposed project. If the financial manager decides not to invest, then the corporation can pay this extra cash out to its shareholders, say as an extra dividend. The shareholders would vote for the company to invest in the new project, if the rate of return offered by the investment project is higher than the rate of return that shareholders can get by investing on their own Investment Appraisal Techniques - utilised to make a decision over whether or not we should invest in a project, as well as to choose between competing projects. Three basic project appraisal techniques: a) Payback period b) Net Present Value c) Internal Rate of Return. Assumed point of cash flow is at the end of each period; but cash flows accumulate over the period. Therefore, we are discounting back from further ahead than we need; and PV calculations tend to be conservative Payback Period (PB) - PB of a project is the number of years it takes before the cumulative forecasted cash flow equals the initial outlay. The payback rule says: 1) only select projects which pay back within the specified time period. 2) choose between options on the basis of the fastest payback. This method ignores later year cash flows and the time value of future cash flows. A modified version, discounted payback, considers TVM but still ignores later year cash flows. PB - Advantages: Easy to calculate, simple to understand, Useful in certain situations 1) Rapidly changing technology (a quick PB is essential when scrapping a new plant) 2) Improving investment conditions (attention is directed to projects which will release funds sooner), It favours projects with a quick return – helps company growth – minimises risk – maximises liquidity, It uses cash flows rather than profit, It can be used as a screening device as a first stage in eliminating obviously inappropriate projects prior to more detailed evaluation PB - Disadvantages: It is not concerned with increases in wealth – it promotes liquidity rather than increased value, It ignores return after the payback period, It ignores the cost of capital and therefore the time value of money, There is objective measure as to what length of time should be set as the minimum payback period Net Present Value (NPV) - NPV is the total present values of each of a project’s cash flows (using a present value discount factor) less the initial investment. The NPV rule states that managers increase shareholders’ wealth by accepting projects that are worth more than they cost. Hence, they should accepts all projects with positive NPV. Step 1 - Use the appropriate discount rate to discount the project’s future cash flows. The sum of these discounted cash flows are the present value (PV) Step 2 - Calculate the NPV by subtracting the cost of initial investment from the PV Step 3 – Make a decision (accept or reject) NPV Assumptions: All cash flows occur at the end of a year. Initial investment occurs at time to. Other cash flows start one year after that (t1). NPV Decision Rule - The NPV represents the surplus funds earned on the project, hence: – If the NPV is positive – accept the project. – If the NPV is zero – the project breaks even (no profit, no loss). – If the NPV is negative – the project should not be accepted. – For mutually exclusive project, the company should choose the one with the highest NPV NPV - Adjusting for Inflation: Cash flows NOT adjusted for inflation = REAL cash flows VS Cash flows adjusted for inflation = Nominal cash flows. Two methods where cash flows presented in real term (in other words, today’s prices): 1) REAL METHOD – do not inflate cash flows, leave them in real terms and discount using real rate. 2) NOMINAL METHOD – multiply cash flows by inflation rate/s and discount using nominal rate. Be consistent: – Real with Real – Nominal with Nominal. Inflation does not affect all costs to the same extent. Where general and specific inflation rates are given – use nominal method in question. NPV - Corporation Tax - Corporation tax is charged to company’s profits: – Operating cash flows will be taxed at corporation tax rate. – Investment spending attracts capital/written down allowances. – Tax normally paid one year in arrears. NPV - Written Down Allowances (WDA) - Depreciation is not an allowable expense for tax purposes. Cost of asset deducted from taxable profits in form of WDA. WDA are calculated using 2 methods: Reducing balance method Straight line method  NPV - Advantages - Considers all cash flows of projects. Allows for the time value of money. Gives an absolute measure, allowing for comparison of projects. It is directly related to the objective of maximisation of shareholders’ wealth (value of the business). It is practical and easy to use (once the anticipated cash flows have been identified – which is difficult to do in reality). It gives clear and unambiguous signals to the decision maker. NPV = best tool NPV - Disadvantages - Difficulty obtaining all relevant costs/benefits. Difficult to calculate and to explain to managers Assumes cash flows occur at annual intervals. The need to estimate a cost of capital Internal Rate of Return (IRR) - The IRR of a project is the rate of discount which, when applied to the project’s cash flows, produces a zero NPV - Decision rule: Accept an investment project if the opportunity cost of capital (let’s call it r) is less than the internal rate of return (IRR). It is called the opportunity cost because if the company decides to invest in this project, it will forgo other similar investment opportunities. True and Estimated IRR - try and get the best estimate using graphical linear interpolation ie. pick one lowest positive NPV and the lowest other NPV 2 and dp the IRR calculation - NPV Y Axis and Discount rate on Y - IRR = on X axis IRR - Advantages - Represents a break-even point. Takes into account time value of money. Considers all cash flows of projects. Is a percentage and therefore easily understood. A company selecting projects where the IRR exceeds the cost of capital should increase shareholders’ wealth IRR - Disadvantages - It is not a measure of absolute profitability. May conflict with NPV decision. Non-conventional CFs (more than one change in direction of CFs) may give rise to no IRR or multiple IRRs. Fails to recognise value; it is only concerned with percentage returns. Assumes cash invested at IRR. Not possible to compare projects if scales of investments are different because small project may have high IRR but actually increase wealth by very little in absolute terms. IRR – Disadvantages (Mutually Exclusive Projects) These are projects in which acceptance of one project excludes the others from consideration. Since NPV is an absolute measure, it will rank a project adding more value higher regardless of the initial investment amount required. IRR, on the other hand, is a relative measure, and it will rank projects offering higher return regardless of the total value added IRR - Payback Reciprocal: Payback reciprocal can be expressed as: 1/Payback. Payback reciprocal is an upper bound for the project’s IRR: IRR ≤ 1/Payback.  Week 3 - Working Capital Management Financial Management Objectives - We should not assume that financial management concerns only long term financial decisions. Short-term assets, such as Inventory, Accounts Receivable and Cash, can be managed to max shareholder wealth NWC = Current Assets - Current Liabilities Short-term (Current) Assets = Inventory + Accounts receivable (trade debtors) + Cash, and short-term securities Short-term (Current) Liabilities = Accounts payable (trade creditors) + Short term debt Increase in NWC = negative free cash flow (outflow); while a reduction in NWC generates a positive free cash flow (inflow). WCM - Objectives - To reduce the amount of inventory held without endangering production. To determine the optimal cash balance. To collect money from customers as quickly as possible. To maintain a good relationship with customers & to take as much credit as possible without endangering supplies. WCM trade-off: Liquidity vs. Profitability - The twin goals of profitability and liquidity will often conflict since liquid assets give the lowest returns. Cash kept in a safe will not generate a return, for example, while a six-month bank deposit will earn interest in exchange for loss of access for the six-month period. Liquidity is needed for a company to continue in business, a company may choose to hold more cash than is needed for operational or transaction needs, for example for precautionary or speculative NWC Measures 1) Operating Cycle = time that elapses from firm’s receipt of raw materials to collection of cash from sale of finished goods & 2) Cash Conversion Cycle (CCC) = is the elapsed time between the points at which a firm pays cash for raw materials and at which it receives cash for finished goods. The difference = the amount of time for which trade creditors are willing to extend credit (TPD) ie. Operating Cycle = IHP + TRD VS Conversion Cycle = IHP + TRD – TPD Components of equations: 1) Inventory Holding Period (IHP) – the average length of time required to convert materials into finished goods and then to sell those goods; it is the amount of time the product remains in inventory in various stages of completion. 2) Trade Receivables Days (TRD) – the average length of time required to convert the firm’s receivables into cash, that is, the time it takes to collect cash following a sale. 3) Trade Payables Days (TPD) – the average length of time between the purchase of raw material and the payment of cash for them + Equations and Current ratios & Acid Test ratios Inventory (Stock) Management Objective - to turn over inventory as quickly as possible without losing sales from stockouts 3 Types of Inventory: 1) Raw Material : The inventory purchased from suppliers that ultimately will be transformed into finished goods. 2) Work-in-Progress: Inventory in various stages of completion; some work-in-process is at the very beginning. 3) Finished Goods: Inventories that have completed the production process and are ready for sale. 3 Inventory - Costs: 1) Ordering costs Making an order and receiving it into inventory … incurred each time an order is placed … e.g. costs of raising purchase requisition, issuing and following up purchase order, transferring goods into inventory, the payment mechanism, accounting, etc. 2) Carrying / holding costs Arise because a certain level of stock holding is maintained / envisaged … e.g. return on funds invested in stock, costs of insurance, storage (rent, rates, light, heat, refrigeration, staff, etc.), cost of stock depreciating or becoming obsolete. 3) Stock-out costs Concern costs incurred owing to having no stock on hand to satisfy customer demand … e.g. loss of contribution because customers go elsewhere, etc Inventory - Management Models: 1) Basic EOQ Model - Total cost minimised when ordering cost = holding cost 2) Stock-Out EOQ Model - Two assumptions: 1) Demand for a given item of inventory is at a constant rate and is known in advance. 2) Lead time (this is the period for order placement and receipt into inventory) is known in advance Basic (EOQ) Model - Issues: Most obvious problem with the basic model is that it ignores “stock-out” costs. Both acquisition lead time and demand for units usually fluctuate in a manner not completely known to the decision maker in advance. Under certainty, re-order point is usage per day multiplied by lead time in days. Needs adjusting → SO EQO Stock-outs (EOQ) Model: Assume deliberate policy of allowing stock-outs. Firm delays reorder beyond the point at which total inventory is depleted. Unsatisfied back orders are made up when new inventory is received. Suppose Q units are ordered, of which S go into inventory and (Q-S) go to satisfy back orders. Just In Time (JIT) System - Imported from Japan. Used to minimise inventory holding cost. The philosophy is that material should arrive at exactly the time they are needed for production. Ideally the firm would have only work-in-progress inventory. This system use no (or very little) safety stock. The goal of JIT system is manufacturing efficiency. It uses inventory as a tool for attaining efficiency by emphasising quality of the materials used and their timely delivery. CASH = funds that a firm holds for immediate payment. These funds include: 1) Cash (the amount of coins and currency); and 2) Marketable Securities (short-term, high-quality debt instruments that can be easily converted into cash). Motives for holding cash: 1) Transaction motive – to conduct normal business transactions. 2) Compensating motive - Firms using bank debt are required to maintain a compensating balance with the bank from which they have borrowed the money. 3) Precautionary motive – Cash flows are unpredictable, hence firms hold cash in reserve for random, unforeseen fluctuations in cash flows. 4) Speculative motive – enable the firm to take advantage of bargain purchases that arise Cash Models - Similar to Inv Models: 1) Basic EOQ Model 2) Stock-Out EOQ Model (Cash EOQ Model with Overdraft)  EOQ Models – Further Issues: 1) Demand (X) for a given item of inventory (or cash flows) is at a constant rate and known in advance Is this true? 2) Holding cost per unit (C) is constant? (Holding cost increases as stock level increases; term structure of interest non-flat) 3) Average balance in stock (or cash) equals to half of order quantity (or transfer amount): constant amount of stock or cash usage daily (seasonal cyclical factors?) Management of Accounts Receivable - Accounts Receivable represent the currently unpaid element of credit sales. Effective management is important because 1) Too much credit is costly in terms of investment in, and maintenance of, accounts receivable. 2) Too little credit could result in the loss of profitable sales. Granting credit should increase profits. Hence, to maximise shareholders’ wealth, a financial manager needs to understand how to effectively manage the firm’s credit activities Reasons why Firms Offer Credit Sales: 1) Industry and Competitive Pressure - It is difficult for firm to offer credit terms that are less generous than their competitors’ offerings. 2) Finance - Certain types of firm have raise finance more cheaply than others. This competitive advantage can be reflected in offering generous credit to customers who experience greater difficulties in raising finance. 3) Efficiency - Information asymmetry exists between buyer and seller. The buyer does not know the quality of the product delivered until it has been thoroughly inspected. The credit period = valuable inspection and verification period The objective of credit management - To collect accounts receivable as quickly as possible without losing sale from high-pressure collection techniques Three main steps: 1) Credit Selection and Standards 2) Credit Terms 3) Credit Monitoring Factoring - Institutions called ‘Factors’ are mainly subsidiaries of the major banks and members of the Factors and Discounters Association. These institutions offer ‘debt factoring services’. Factoring involves raising immediate cash based on the security of the company’s debtors, thus accelerating payment from customers. The factor pays (usually) 80% of the face value of an invoice to the client immediately and the balance less interest and charges when the account is finally settled by the customer A factor provides three main services: 1) sales administration 2) credit protection 3) provision for finance.  Week 4 - Portfolio Theory I: Markowitz Frontier Importance of Risk-Return Relationship: 1)To determine appropriate risk-adjusted discount rates for NPV analysis. 2) Useful for investors (that invest safely in a bank, but also in risky shares and bonds). 3) Useful for corporations (that issue shares to finance themselves). 4) Useful for financial intermediaries (that lend, invest, borrow on behalf of their clients) Return is the total gain or loss experienced on an investment over a given period of time - Investors receive their returns from shares in the form of dividends and capital gains/losses. + Annual Return Equation Risk = possibility that actual future returns will deviate from expected returns (i.e., risk represents the variability of returns). Risk measured by the variance or standard deviation of possible returns around the expected return: – the greater the dispersion, the greater the risk, the greater the variance or standard deviation - and where there is no dispersion of possible returns, then the expected return is a certain return = no risk = 0 variance and standard deviation = Risk-free assets Risk free asset: government bonds held to maturity – (Certainty over the amount and timing of cashflows). Vs Risky asset: – For example, a share investment, which offers a return in the form of dividend and capital gain (both the dividend and the future sale price of stock are uncertain, therefore risky return). Risk preferences of investors: 1) Risk-loving: investor would choose the project with the higher level of risk e.g. investors who enjoy a gamble. 2) Risk-neutral: would have no preference, and the fact that one project has a higher level of risk would not be an issue e.g. investors who are indifferent to risk. 3) Risk-averse: investor choose the project with the lower level of risk. Risk aversion - Most people may be risk-averse over larger investments (house, car etc.,), but risk-loving over small investments (for instance, a weekly lottery ticket). Most investors committing large sums of money to developing an investment portfolio are risk-averse. Risk and Return Approaches – One Asset/Share: 1) The historical approach – based on historical data (e.g. historical stock returns). 2) The probabilistic approach – Based on the concept of probability distributions (shows the possible unique outcomes and their associated probabilities). 3) The risk-based approach – Capital Asset Pricing Model (CAPM) One Asset/Share (Risk and Return - The Historical Approach) - Using historical data (returns), 1) Mean or Average return can be estimated + Equation with n-1 on bottom 2) Variance and 3) Standard Deviation of returns using historical data One Asset/Share (Risk and Return – The Probabilistic Approach) - A probability distribution shows the possible unique outcomes and their associated probabilities. Probability distribution - The measure of central tendency of returns (used) is the arithmetic mean return (the expected return). Measure of dispersion = variance (square root = StDev) Given the probability distribution of returns we can compute the Expected Return = The Expected (or mean) return is calculated as a weighted average of the possible returns, where the weights correspond to the probabilities. Covariance can be used to understand the direction of the relationship between variables. It can range from positive infinity to negative infinity. Positive covariability = returns of two assets tend to move in the same direction. A function of the covariance, the correlation coefficient measures both the 1) direction and 2) strength and of the linear relationship between the two variables. A correlation coefficient of +1 indicates perfect positive correlation, such that the returns of the two shares will vary in perfect lock-step - Most shares are positively correlated with each other. A negative correlation coefficient, which is less than 0 but greater than -1 = tendency for the returns to move in opposite directions. A correlation coefficient of 0 indicates that there is no relationship between the two assets in terms of the variability of their returns. A zero-variance portfolio can only be constructed if the correlation coefficient between assets is -1 + EQUATIONS = covariance of a 2-stock portfolio = correlation coefficient times SD A stock’s returns times the SD of the other stock’s returns TOTAL RISK = SYSTEMATIC RISK + UNSYSTEMATIC RISK Systematic Risk (also called Nondiversifiable Risk, or Market Risk) refers to that portion of the variability of an individual security’s returns cause by factors affecting the market as a whole (e.g., interest rate changes; inflation etc.). Unsystematic Risk (also called Diversifiable Risk, or Unique Risk) is risk that is unique to the firm (factors causing it: management capabilities and decisions; strikes; the availability of raw materials; foreign competition etc.). Risk Diversification - Because, unsystematic risk (firm specific) could be reduced or even eliminated, most investors tend to invest in a group of assets (portfolios) rather than a single one. Hence, diversification is a strategy designed to reduce risk by spreading the portfolio across many investments. Diversification is mathematically sound: – Most people are risk-averse. – People take risks only if they believe they will be rewarded accordingly for taking them - randomly selected 15 to 20 different securities will do the job!(eliminate 90% of unique risk)- Diversifying = reduce total risk by reducing unsystematic risk Portfolio Definition - a collection of assets (stocks, bonds, etc) - sum of which equal to 100% Portfolio theory - It makes certain assumptions and it derives the optimal combination of risky assets given their characteristics. Key = good idea to have all your investment funds in one asset (not all eggs in one basket) By investing funds in a portfolio (in 2+ assets) you increase the possibility of improving Return relative to the Risk being taken. The risk of the  portfolio is less than the weighted average risk of the individual constituent investments. Risk can be reduced through diversification without an associated reduction in returns. Portfolio Assumptions - 1) Investors make investment decisions in a single time period framework. This can be one week, one month, one year or longer. 2) Investors prefer more money to less money. 3) Investors are risk averse: they require extra return for extra risk. 4) Investors measure return by expected return and measure risk by standard deviation of returns Key - investors should aim to invest in a portfolio with assets that have a correlation coefficient of -1 (as negative as it can be) as this will maximise reducing risk (reducing variance) - this does not guarantee risk 0 To guarantee zero variance (zero risk: you need 1) -1 Correlation + 2) Optimal Proportions = 0 Variance (no risk) Variance-Covariance Matrix - Variance of Asset 1 & Asset 2 portfolio is the sum of variance-covariance matrix for those assets. As long as the correlation coefficient (ρ) is less than perfect positive (+1), the standard deviation of a portfolio of two assets is less than the weighted average of the standard deviations of the individual assets. The Feasible (Opportunity) Set - the Feasible Set is the set of investment opportunities and can be found by calculating the Expected Return and Standard Deviation for a portfolio of two risky assets with varying weights (graph) Power Correlation all together - The lower the correlation, the more bend in the curve. The lower the correlation, the more bend in the curve (-1). Where the correlation coefficient between portfolio components is greater than -1 (but less than +1), risk reduction is possible, but total risk elimination is impossible. Expected Return = X axis and Standard Deviation = Y acis The Feasible Set - Multi Asset Portfolios - We consider N assets: – with varying degrees of correlations between their returns. – Each can be plotted on the mean-std deviation diagram. – Each subset of them can be formed into a portfolio, with. – Any set of portfolio weights. Repeating this will all possible combinations of assets leads to the feasible set of N assets. All possible portfolios that can be constructed from just two assets (with a specified correlation coefficient) can be illustrated graphically as lying along a line, but when dealing with multi-asset portfolios, all possible combinations = shaded ‘area’. Portfolio Dominance - A situation in which investors universally prefer one alternative over another - all rational (risk-averse) investors will clearly prefer one alternative. A portfolio dominates all others if 1) for its level of expected return, there is no other portfolio with less risk 2) for its level of risk, there is no other portfolio with a higher expected return. Those portfolios that are not dominated constitute the Mean Variance Efficient (MVE) frontier. For 2 Asset Portfolios - Feasible Set = all possible portfolios of securities. MVE Frontier = set of portfolios that have highest expected return for any given level of risk (upper half) MV-X For Multi-Asset Portfolios - Whole curve = MF: Markowitz Frontier and Upper half = MVE: shaded area represents all possible combinations of expected return and standard deviation for a many-asset portfolio. A single curve (earlier) vs. an entire area. A rational, risk-averse investor will only invest somewhere on the upper edge between MV and X. Minimum Variance Portfolio - most left part of the efficient frontier (MV) Optimal Portfolio For An Investor - (Utility Theory & Risk-Averse Investor): Utility is the level of satisfaction that an individual derives from some desirable factors. Utility levels of it are frequently represented graphically by utility curves (or indifference curves), each one showing a constant level of utility or satisfaction for differing combinations of related factors. An investor’s utility curves =combinations of expected return and risk that are equally preferable to the investor. There is a utility curve for each level of utility. The investor is indifferent to every point on a particular utility curve, because every point generates the same utility for the investor. Investor Utility - Portfolio theory assumes investors are risk-averse - shape of utility curve depends on level - more risk-averse investor = steeper as requires a larger increase in expected return to compensate for bearing an extra unit of risk. Optimal Portfolio for a Risk-Averse Investor - The optimal portfolio for an investor, therefore, is the point of tangency between the MVE frontier and investor’s utility curve. At this point of tangency, the cost of an additional unit of expected return is equal to the price that an investor is willing to pay for it  Week 5 - Portfolio Theory II: CML and CAPM So far only considered portfolios of risky assets = What if we construct a portfolio with one risk-free asset + one risky asset Risk Free Asset - Provides risk-free rate of return = the return is known for certain and no variability.–Has zero standard deviation.–Has zero correlation with all other risky assets.–Offers risk-free rate of return, which is the minimum return required by all investors for an investment whose returns are certain. Eg. treasure bills or short-term government bonds Risk Free + Risky Asset Er, Std, Covariance, Coefficient: Covariance - the covariance of the risk-free asset with any risky asset or portfolio will always equal zero. Similarly, the correlation between any risky asset and the risk free asset would be zero. Expected return: a linear relationship - Standard deviation of the portfolio is the linear proportion of the standard deviation of the risky asset. In addition to the feasible set of risky assets, an investor can combine any risky asset (or portfolio) A with the risk free asset Rf new portfolio to create a new portfolio. The new portfolio will lie on a straight line connecting the risk free asset Rf to the risky asset A. The different portfolios that are available from combining the two investments lie along a straight line because when combining a risk-free and a risky investment, portfolio risk becomes a simple weighted average of the risk of the components. Portfolio Dominance - Suppose that an investor is faced with a choice amongst many alternative risky investments. The shaded area represents all possible risky investment portfolios open to her, and AB represents the efficient set of portfolios available. Combinations of government stock (rf) and portfolio D dominate all the rf and C portfolios, as well as all those portfolios from B to D on the original risky portfolio efficiency boundary. Lending at the Risk Free Rate - The original efficiency boundary A-B has now been modified to A-M-r f. An investor who wishes to locate somewhere along A to M has to specifically identify the particular portfolio of risky investments. An investor who wishes to locate along M to rf will place a proportion of her investment funds in government bonds (lending) and the remainder in risky portfolio M. Investors will no longer be interested in any portfolio lying along M to B as these are all dominated by portfolios lying along the risky-riskless boundary of M to rf Lending or Borrowing at the Risk Free Rate - Assume that all investors can lend and borrow unlimited amounts of cash at the risk-free interest rate. Lending or borrowing at the risk-free rate allows investors to achieve the returns beyond the efficient frontier. Investors now would be interested in holding only one optimal portfolio of purely risky assets: market portfolio M, which consists of shares in all the companies quoted on the stock exchange. The line connecting rf and M is called the Capital Market Line (CML). Given the above assumption, the best investment portfolio is combining market portfolio and risk-free asset (lending or borrowing) according to one’s risk appetite. Therefore, investors with different risk preferences will all hold the same risky portfolio of shares (i.e., portfolio M) but will have different proportions of borrowing or lending Moving Along the CML: 1) Lending zone - Investors who wished to locate on the CML somewhere between r and M would invest a proportion of their funds in that portfolio of risky assets represented by M, and the remainder of their funds would be placed in the risk-free security 2) Borrowing zone - Investors who wished to locate on the CML above M would place all their own investment funds in the portfolio of risky assets M, borrow additional funds at an interest rate of rf, and invest those additional funds also in M Individual Investor’s Optimal Portfolio - For an investor, the optimal portfolio is the point of tangency between the investor’s utility (indifference) curve and the new feasible set The Market Portfolio and The Capital Market Line (CML) Market portfolio is the portfolio containing all risky assets in proportion to their market value. An investor who wishes to hold the market portfolio as part of her overall investment portfolio would hold shares in all the companies quoted on the stock market, in amounts proportionate to their total market values + example The Market Portfolio –A Proxy - A broad-based equity portfolio, such as the FTSE100, S&P500, Nikkei 225) could be a proxy for the market portfolio in practice (this includes academic or professional empirical work). Several studies have also shown that constructing a randomly selected portfolio of shares consisting of only between 15 and 20 different securities results in the elimination of around 90% of the maximum amount of risk that it would be possible to eliminate through diversification. As a result, it is relatively easy to hold a portfolio of risky assets that closely resembles the market portfolio in terms of both risk and expected return  Market Portfolio -Equilibrium Market Prices - The concept of the market portfolio produces a definition of equilibrium market prices. If the market portfolio contains the shares of all the quoted companies, then the market prices of those shares must be such that they are acceptable investments for inclusion in the market portfolio. In other words, share prices are at equilibrium when they produce an expected return that is just sufficient compensation for the risk that they involve. The Market Portfolio –Well Diversified - Note that, given the risk reduction effect of diversification, M represents the ultimate diversified portfolio: all the risk that is possible to eliminate, has been eliminated. In other words, all the unique (unsystematic) risk of individual assets is diversified away (well-diversified). Because portfolio M lies at the point of tangency, it is on the highest portfolio possibility line. Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML The Capital Market Line (CML) - provides a risk-return relationship and a measure of risk for all efficient portfolios (i.e., portfolios that do not posses any diversifiable risk). The appropriate measure of risk for an efficient portfolio is the standard deviation of return of the portfolio. There is a linear relationship between the risk as measured by the standard deviation and the expected return for these efficient portfolios. All efficient portfolios would lie along the CML. All portfolios other than the efficient ones will lie below the CML. The CML does not describe the risk-return relationship of inefficient portfolios or of individual securities. The market portfolio represents point on efficient frontier that maximises the slope of the CML. The Capital Market Line -Assumptions: 1. The investor’s objective is to maximize wealth. 2. Investors make choices on the basis of risk and return. Return is measured by the arithmetic mean return from a portfolio of assets, and risk is measured by the standard deviation of those returns. 3. All investors can lend and borrow unlimited amounts of cash at the risk free interest rate. 4. No taxation, transaction costs or other market imperfections. 5. All investors have the same knowledge and expectations about the future and have access to the complete range of investment opportunities. Investors are all price-takers and have free access to all relevant information. 6. All investors have the same decision-making time horizon. + Slope and Formula of CML Total Risk and Diversification: Total Risk = Systematic risk + Nonsystematic risk. Our analysis indicates, that as more securities are added to a portfolio, the unsystematic risk is reduced. For a very well diversified portfolio, unsystematic risk tends to become zero and the only relevant risk is systematic risk. Hence, the risk-return relationship is not based simply on the total risk of individual investments (the variability of their possible returns) but on just one part of that risk: the systematic risk(this is market risk). Investor Risk Bearing - Investors will only be compensated for bearing systematic Risk. In other words, the market would not provide a reward (in terms of an increased expected return) for that part of an investment’s risk that could be eliminated by holding it as part of a well-diversified portfolio. For instance, we can expect that in a portfolio, the bad luck associated with one company will be balanced by better luck for others. However, an increase in the level of corporate taxation or a rapid rise in interest rates will adversely affect all firms and there is no offsetting effect. Beta (β) is a measure of the systematic risk. The parameter βj tells us the sensitivity of the return on stock j to the return on the market portfolio. Beta Value greater than one indicates higher sensitivity to the market changes. Beta Value less than one indicates lower sensitivity to market changes. Interpreting Beta - The numerator of the beta value (σjρjM ) represents the systematic risk of company j, and the denominator(σM) represents the total risk of the market portfolio which is all systematic risk. Hence the beta value of company j shares is an index of the amount of company j’s systematic risk, relative to that of the market portfolio High beta shares (i.e. where β> 1) will tend to outperform the return on the market portfolio (the return on the FTSE Index) and low beta shares (i.e. where β< 1) will tend to under perform the average return on the stock market. But this under-or over performance comparison with the return on the market portfolio applies to both rises and falls in the return on the market portfolio. Therefore high beta shares can either be a good or a bad thing, depending on what is happening to the return on the FTSE Index Security Market Line (SML) - The Security Market Line gives the expected return from an ‘inefficient’ investment, such as a risky portfolio other than the market portfolio or, more importantly, an investment in the shares of a single company. The expected return on any inefficient investment is determined only by its non-diversifiable risk, so the SML only considers the level of systematic risk, beta. SML and CAPM - Hence, the SML gives a linear relationship between Beta and expected return, and the equation of this line is the fundamental risk and return relationship predicted by the Capital Asset Pricing Model (CAPM). CAPM says that the expected return from asset j equals to the risk-free return, plus a market risk premium determined by the market price of (systematic) risk and the systematic risk level of firm asset j. Market risk premium is the additional return earned (or expected) on the market portfolio over and above the risk-free rate. A model that gives the relationship between expected return and systematic risk is known as an Asset Pricing Model, and the CAPM is the most important equilibrium pricing model.  CAPM is an equilibrium model seeking to explain why different assets have different expected returns. SML is the basis and the graphical representation of the CAPM The SML is the graphical representation of CAPM. The expected return on a security with a beta of 0 is equal to the risk-free rate. The expected return on a security with a beta of 1 is equal to the expected return on the market (indicates that the security moves at the same rate and in the same direction as the market) Using SML for Valuation - In equilibrium, all assets and all portfolios of assets should plot on the SML - if above line = underpriced - This is because its current price is too low relative to expected future price so that the forecast return is too high. CAPM -Assumptions - No transactions’ costs. All assets are infinitely divisible. No personal taxes. Capital asset markets are purely competitive. Investors choose portfolios based solely on expected return and standard deviation of such returns. Short sales are permitted. Unlimited lending and borrowing at the risk free rate is permitted. Investors have homogeneous expectations regarding asset returns, and variances and covariances of such returns SML versus CML - Both, CML and SML postulate a linear (straight line) relationship between risk and return. Risk: in CML the risk is defined as the Total Risk and is measured by standard deviation; in SML the risk is defined as systematic risk and is measured by Beta. CML is valid only for efficient portfolios; SML is valid for all portfolios and all individual securities, whether efficient or inefficient. CML is the basis of the Capital Market Theory; SML is the basis of the Capital Asset Pricing Model (CAPM). Slope: CML, market portfolio Sharpe ratio; SML market risk premium. Definition: CML graph of efficient frontier; SML graph of the CAPM. How Useful is the CAPM Model? The CAPM model is one of the most important models in all finance. Financial managers use the model to establish required rates of return on all types of investment projects. The model helps managers understand what returns market requires on projects having different risk levels. This is an important knowledge to improve the quality of corporate investment decisions. However, there are limitations to the CAPM model. CAPM -Limitations - It is a single factor model. It makes unrealistic assumptions. The parameters of the model cannot be estimated precisely (for example, parameters used to in determining the risk-free rate of return and beta value). The model assumes a linear relationship between its variables. CAPM –Empirical Evidence - There does appear to be a positive linear relationship between beta and the investment’s return. So, fundamentally, we could conclude the CAPM does appear to be correct: high beta shares give high returns, and low beta shares give low returns. The actual slope of the CAPM appears to be slightly less than the predicted slope. In other words, low beta shares (those with < 1) tend to give slightly higher returns than CAPM would predict, while high beta shares (> 1) tend to give slightly lower returns than CAPM would predict. Despite the above, the arguments should be kept in perspective. Although the CAPM is not perfect, it probably is a fairly good predictor of returns and it is certainly better than anything else that is available. Although there may be a number of other factors (e.g. company size and dividend policy) which go towards determining returns, it still appears that relative systematic risk (beta) is by far the most important of these factors. + An Economy with Two Assets only Example