FNCE30001 Investments (CONCEPTS) PDF

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LECTURE 2: ASSET ALLOCATION Why is the tangency portfolio the best portfolio to combine with the risk free? The combination of the two is the combination of debt and equity that will yield the highest sharpe ratio, and hence the highest expected return for a given level of risk. This therefore means...

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LECTURE 2: ASSET ALLOCATION Why is the tangency portfolio the best portfolio to combine with the risk free? The combination of the two is the combination of debt and equity that will yield the highest sharpe ratio, and hence the highest expected return for a given level of risk. This therefore means that it is the highest utility portfolio.

LECTURE 3: SECURITY SELECTION For Modern portfolio theory we want to find the portfolio (ie the weights) that give us the lowest standard deviation for a given target expected return. Problems with Markowitz theory  The optimal portfolio is speculative because you will take extreme positions on estimates which will involve a lot of errors – the outcome is by no mean certain as target return is not the return of the investor.. This is why in many circumstance the equally weighted portfolio (1/N) method will be more effective as it will be appropriate for all outcomes.  The success of the portfolio will be depended on the quality of the ‘input list’ – estimates of the expected security returns and the covariance matrix.  Relies on history repeating itself and estimates being correct which is very rare. Solutions to these problems 1. Apply constraints – this is done so that you can take less extreme positions in securities and reduce tour exposure to certain scenarios occurring. Eg no more than a certain amount of short selling, or no more than a particular amount in a security or market. 2. Shrinkage – this means that you do not fully believe the estimates that you get form the data, but you combine the estimates with numbers that capture more central tendencies to avoid extreme tendencies. You pull some of the more extreme estimated coefficients towards more central values 3. Use factor models to obtain expected returns and covariance matrix 4. Bootstrap – the basic idea about bootstrapping is that inference about a population from sample data (sample population) can be modelled by resampling the sample data and performing inference on resampled samples.

LECTURE 4: CAPM Returns under the capm theory are essentially compensation for bearing systematic risk. Idiosyncratic risk is not considered as it is wiped out by diversification  The SML graphs individual asset risk premiums as a function of the beta  The CML graphs efficient portfolio risk premiums as a function of standard deviation. It is a special capital allocation line – the CAL obtained with market portfolio.  If the CAPM is valid, the expected rate of return compensates only for systematic risk (measured by beta).  Beta will measure only systematic risk, whereas sigma will measure total risk, as the risk has not been diversified away. Assumptions 1. All investors use the Markowitz portfolio selection model 2. All investors share the same economic view of the world, they derive the same input list ( μ and V) 3. All investors plan for one identical holding period (same investment horizon) 4. Investments are limited to a universe of publicly traded financial assets. In reality large frictions make segmented markets (like trying to buy an American stock from Australia) 5. Investors may borrow or lend any amount at a fixed risk-free rate 6. Investors are price takers, they act as if security prices are unaffected by their own trades. 7. Investors pay no taxes on returns and there are no transaction cost Implications 1. All Investors will choose to hold the market portfolio. (the market portfolio will be the one with the highest sharpe ratio and tangent to the optimal capital allocation-line, the capital market line) 2. For individual securities – The risk premium on the individual assets depends on Beta and the market premium

3. The market portfolio will be the tangency portfolio (Highest sharpe ratio) to the optimal CAL. All investors holder the market portfolio as their optimal risky portfolio, differing only in the amount invested in it versus the risk free rate. Problems with the CAPM model  “sensitivity of beta” – Beta is effected by a few things eg which stock is used as the market reference, the historical period and the frequency of returns  Betas are time varying (firms change over time and their risk does as well)  Betas are very hard to estimate, precisely there are high standard errors. Differences between SML and CML  SML describes relationship between expected return and systematic risk (Beta on x axis)  CML describes relationship between expected return and total risk (standard deviation on x axis)  To calculate the slope (ratio of risk premium to Beta) for a stock: E(r)-Rf/its beta. LECTURE 5: APT Like the CAPM the APT model predicts the security market line linking expected returns to risk. In the APT Model,  = E(r) – Rf which is the risk premium for each factor, which will also be the slope of the security market line Single Factor model  The unanticipated component of the factor model, e, is a random variable, it will sometimes be good and sometimes be bad therefore we assume that on average e = 0  The common factor (F) is a macroeconomic variable that affects all firms, where beta is the sensitivity of this firm to the particular factor. The common factor is random like the unanticipated component (Sometimes good sometimes bad) so we assume on average E(F)=0.  Cov(F, e) = 0  α=r i− r m . If alpha is positive then the market is under-priced, if it negative then it is overpriced. Assumptions of the model 1. Security returns can be described by a factor model 2. Idiosyncratic risk can be diversified away 3. Markets are perfectly competitive Differences between CAPM and APT  The APT can only be applied to well diversified portfolios  It is silent on the number and identi Conditions of Arbitrage  There must be no net wealth invested (Ie if you invest in something you must always short something else to even it out)  All the Betas will add to zero (there is no systematic risk)  There will be an overall positive return. LECTURE 6: ZERO COUPON BONDS  The price will depend on the affect of the remaining maturity and the interest rate.  The effect of time is deterministic, while the effect of interest rates is stochastic. GDP to Debt Ratio The GDP to debt ratio measures what a country owes versus what it produces – it indicates the ability of the country to pay back debt. South America, South east Asia and India have a low ratio. While Australia has a AAA rating.

LECTURE 7: BOND PRICING

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If coupon rate = market rate then the P0 = Par. Coupon and Par value do not change, while remaining maturity and interest rates do. Therefore the price will depend on the joint affect of the remaining maturity and the interest rate. The price of the Bond will converge over time to equal Par at maturity – this is only the case if interests remain constant.

If we are dealing with a coupon bond, total return = YTM ONLY if: 1. The bond is held to maturity 2. Coupons can be reinvested at the same rate as ytm Why do bond prices react to interest rate fluctuations In a competitive market, securities must be offer fair expected returns for investors. If a bond is issued at 8%, when competitive market yields are 8%, then the bond will be fairly priced. However if market returns 9% then the 8% return will be no longer attractive for investors, the bond price will then fall until its expected returns increase to 9% The opposite applies. Say 8%>7%, the coupon rate is attractive so investors will respond by bidding above par value until the return back to the market rate of 7%. Price effects of Coupon bonds  Higher par value -> higher cash flow to buyer -> higher price  Higher coupon rate -> higher cash flow to buyer -> higher price  Longer maturity -> higher the discount of PVt -> lower price  Higher interest rate -> higher the discount of PVt -> lower price Evolution of prices for Coupon bonds 1. Price of bond when issued is equal to par value 2. Negative relationship between price and yield 3. Volatility reduces as you reach maturity 4. Whenever interest rate is equal to coupon rate, the bond is at par 5. At maturity, price is par value Relationship between Coupon rate and Interest rate Coupon rates with a higher rate than the market interest rate will be valued much higher than others as the payoff is greater for investors.  Coupon rate remains the same, however yield changes depending on the price. Lower price = higher yield. So when there is higher yield demand will push the price up until the yield equals the market rate once again. LECTURE 8: YIELD CURVE  The long term interest rate should be higher in comparison to the short term rate, as investors require a higher rate of return in order to compensate for the longer term to maturity Normal curve: Investors temporarily invest in short term bonds in the hope of purchasing long term bonds in the future for higher yields. The short term increase in demand for short term yields drives the price down. Inverted: When the economy transitions from up to down, due to higher demands, yield on the long term bonds will fall, creating an inverted yield curve. Two arguments to inverted yield curve  If investors sense instability in the market they will increase their purchases of interest bearing securities, if interest is likely concentrated in longer term rather than shorter term securities. This will result in the falling of the long term rate and an inverted yield curve, because higher demand will reduce the yield.  During recessions Central banks cut interest rates to stimulate growth. If a recession is imminent, the investors may expect lower short term interest rates in the future, which will reduce the slope of the yield curve. Facts 1. Interest rates are persistent and non-negative

2. Interest rates are effected by Mean-reversion: the rates tend to decrease when above the mean and increase when below the mean 3. Changes in interest rates are not perfectly correlated 4. The volatility of short term interest rates is higher than the volatility of long term rates – as maturity increases, volatility decreases. Expectations Theory  Under the expectations theory, there will be no uncertainty and expectations are fulfilled  Investors are also risk neutral and do not care about risk  Investors are indifferent between holding the investment for the 2 year spot rate and rolling as the holding period will be the same. Three implications 1. The slope of the yield curve is attributable to expectations of changes in short term interest rates. If you observe long term interest rates are higher than short term we expect interest rates to increase 2. The holding period return on bonds of all maturities ought to be equal E [ HPR0 , t ]=r 0 ,t 3. The forward rate equals the expected short term interest rate. The market sets today’s zero rate such that today’s forward rate equals expected returns E [ r t , T ]=f t ,T Liquidity Theory We introduce risk aversion and this removes perfect foresight. The future can be different from our expectations  We expect that the forward rate will exceed the expected short-term interest rate for that year Three implications 1. Slope of the yield curve depends on expectations and risk premium required by investors E ( hpr 0 , t)=r 0 ,t + premium 2. 3.

f t ,T =E ( r t ,T ) + premium

Liquidity vs Expectations  As yield to maturity increases, the premium will increase. Market segmentation theory  Bonds of different maturities effectively trade in different markets, each with its own supply and demand forces that produce bond yields.  The market for each segment of bond maturities consists mainly of investors who have a preference for investing in securities with specific durations. LECTURE 9: MANAGING BOND PORTFOLIOS  Fabio Grosso was the person to score the last free kick in the world cup Risks Returns (the three things we examined earlier in the course: market value from selling, cash flows received, income from reinvesting cash flows) will be subject to uncertainty due to:  Credit risk  Liquidity risk  Inflation risk  Exchange rate risk  Interest rate risk  Reinvestment risk. Interest rate sensitivity the relationship between change in yield and change in price is CONVEX and not linear, so we have the following laws as to what effects the convexity of the graph. 1. Bond prices and yields are inversely related – as yields increase bond prices fall and vice-versa 2. An increase in Bond’s yield to maturity results in a smaller price change than a decrease on yield of equal magnitude

3. Price of long term bonds tends to be more sensitive to compared to short term bonds in terms of interest rate changes 4. The sensitivity between prices and yields increases at a decreasing rate as maturity increases 5. Interest risk is inversely related to the bond’s coupon rate. Prices of low coupon bonds are more sensitive to changes in interest rates rather than prices of high coupon bonds. 6. The sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the bond is currently selling lower YTM -> Higher sensitivity.

Relationship between prices and interest rates  Negative (Law 1)  Convex (Law 2)

Sensitivity to interest rates depends on  Time to maturity (Law 3 and 4) (+)  Coupon rate (Law 5) (-)  Initial yield (Law 6) (-)

Duration Allows us to quantify the sensitivity to interest rate risk, so we use duration which is ‘the weighted average of times to each coupon or principal payment’.  The duration of a zero coupon bond will always equal its times to maturity What determines duration? 1. The duration of zero coupon bonds equals its time to maturity 2. Duration is positively related to maturity 3. Duration is negatively related to coupon rate 4. Duration is negatively related to yield to maturity Strategies for managing Bond portfolios Passive strategies:  Indexing – essentially you will choose to either adopt perfect replication (will exactly mimic the index), or stratifying the bond portfolio (dividing the index into different cells with each one representing different characteristics, like duration, coupon rate or credit rating.  Immunisation – means to ensure that the bond portfolio a target rate or return, even if yields change. The aim to have a portfolio of bonds which is not dependent on changes in interest rates. You are exposed to uncertainty, however if you buy a bond with duration exactly equal to time, T, you will be immunised Active strategies:  Trading on market inefficiencies – Based on the belief that yield relationships between bonds or sectors is temporarily out of alignment. Until the difference is eliminated gains can be realised on the under-priced bond (arbitrage). HOWEVER, it is 1) not easy to find perfect substitutes, 2) there are transaction costs that will impact on returns, 3) Differences are so tiny they require a lot of leverage to make them profitable, and 4) short selling is costly.

LECTURE 10: INSTITUTIONAL INVESTORS AND PERFORMANCE EVALUATION Institutional investors

Why can’t we just use past returns to assess performance? 1. There is a positive relationship between risk and return 2. A portfolio manager who takes too much risk might not survive Reason 1 + Reason 2 = the higher the risk taken the higher the performance, the lower probability of survival! Why do the Sharpe and Treynor ratios serve different purposes? When we combine two assets we should use the treynor ratio, to find the optimal weight between the risky assets and the risk free asset. When we combine assets we want to choose based on beta because the lower the beta, the higher the reduction of risk. We will decide to use the sharpe ratio when we are deciding to split between the risk-free asset and one risky asset. What is the purpose of measuring Alpha, does a positive one correlate to good manager skills?  In deciding whether or not to invest money and how much to invest in a fund its crucial to figure out how much the value the fund managers actually add.  Jensen’s Alpha can be interpreted as the maximum you should be willing to pay in order to compensate a fund manager Market Timing Market timing is a strategy of making buy or sell decisions of financial decisions by attempting to predict future market price movements.  Implied by a belief that not all new information is not immediately incorporated into the price of the asset....