Risk and Return from Historical Record PDF

Stuvia - Koop en Verkoop de Beste Samenvattingen Chapter 2: Risk and return from the historical record Portfolio theory breaks investments down mainly to risk and return. Return: the amount of money gained or lo...

Stuvia - Koop en Verkoop de Beste Samenvattingen Chapter 2: Risk and return from the historical record Portfolio theory breaks investments down mainly to risk and return. Return: the amount of money gained or lost on an investment relative to the amount of money invested. Which factors do impact the interest rate? Supply of capital: by households Demand of capital: by businesses Government’s net supply and/or demand: actions by the ECB C OMPARING RETURNS : ZERO COUPON BONDS Assume that you have the choice between several zero-coupon bonds with different maturities and a par value of 100. How can you compare them? The return that you get is the holding period return over the period from t=0 to t=T. It is a bit like an interest rate that you get throughout the period. The difference is that a normal interest rate is fixed at the beginning. PT P T −Pt HPRt = –1= Pt Pt Pt = price today  initial investment PT = price at the end of the holding period  final payout HPRt = holding period return BOND TIME TO MATURITY PRICE Pt HPRt A 1 90 (100/90) – 1 = 0.11 B 5 80 (100/80) – 1 = 0.25 C 10 70 (100/70) – 1 = 0.43 The holding period returns increase for bond A to C. this does not necessarily mean that bond C is better than the others. We can’t compare these bonds because they holding periods differ. The holding period return is a good measure ONLY if the holding period is the same for all assets under consideration. Otherwise we need to normalize the returns by the holding periods. You can do that by calculating ‘one-year-equivalent-returns’. Gedownload door: hannahducatteeuw | [email protected] Wil jij4€76 per Dit document is auteursrechtelijk beschermd, het verspreiden van dit document is strafbaar. maand verdienen?  Stuvia - Koop en Verkoop de Beste Samenvattingen HPR (1+ EAR)T −1 A simple way is to use the annual percentage rate: APR = = T T T = time to maturity However, the APR does not consider re-investments, if you would reinvest the money you would get different results at the end. Assume you buy bond B for €80, after 5 years you get €100 back so you have earned €20. If you would reinvest in the same bond immediately, you would now be able to invest €100 which is 1,25 times what you previously invested. This will lead to a payout of €125 instead of €120… To account for that you can use the effective annual rate: EAR = (HPR + 1)1/T - 1 TIME TO PRICE Pt HPRt APR EAR MAT. 1 90 (100/90) – 1 = 0.11 0.11/1 = 0.11 (1+0.11)1 – 1 = 0.11 5 80 (100/80) – 1 = 0.25 0.25/5 = 0.05 (1+0.25)1/5 – 1 = 0.0456 10 70 (100/70) – 1 = 0.43 0.43/10 = 0.043 (1+0.43)1/10 – 1 = 0.0364  If the time to maturity > 1: EAR < APR The longer to maturity, the larger the difference between the two. P 1−P0 + D1 Holding period return can also be calculated by using dividends: HRP = P0 T HE RELATION BETWEEN INTEREST RATES AND INFLATION Fisher-equation: rnominal = rreal + πexpected  π = expected inflation rate If you lend money to someone you ask a compensation because you have to wait until you get your money back before you can use it yourself. You also ask a compensation because you take a risk by giving someone your money. And you also ask a compensation for the possible loss of purchasing power. If you give away €1000 for 10 years, and you compare what you can buy with that money now and in 10 years then there will be a difference due to inflation. The real interest rate is more important for the investors than the nominal one. But the real interest rate is not known in advance. Interest rates are a compensation for giving away the savers money, it can’t be used for consumption until it is paid back. If inflation is high, lenders may ask a compensation. M EAN SCENARIO OR SUBJECTIVE RETURNS Until now we worked with historical returns which we can simply read from the data. But some investments concern the future, you need to estimate those. Sometimes it is possible to define some scenarios/states for the future and assign probabilities to each of these scenarios. P ERCENTAGE VS. LOGARITHMIC RETURNS Gedownload door: hannahducatteeuw | [email protected] Wil jij5€76 per Dit document is auteursrechtelijk beschermd, het verspreiden van dit document is strafbaar. maand verdienen?  Stuvia - Koop en Verkoop de Beste Samenvattingen Logarithmic returns offer some advantages: Easy calculation (temporal aggregation): Easily aggregate returns to lower frequencies by summarizing high frequency returns. This means we can use the monthly return as the sum of the daily logarithmic returns Symmetry (up and down): Logarithmic returns will give the initial price after a price increase of e.g. 10% followed by a decrease of 10%. See book p.27! Symmetry (exchange rates): Specifically, for exchange rates the return in price quotation and indirect quotation only differs by sign, not in magnitude. M EAN AND VARIANCE OF HISTORICAL RETURNS If we look at the past, there are no scenarios but there is however a lot of variation. Returns are not constant over time, they change almost every period. So how can you get some information about the probability distribution of returns based on historical data? You can simply assume the distribution is normal. In this case you would only need standard deviation/variance and the mean to describe the distribution! S HARPE RATIO Knowing the return and the variation of returns doesn’t help a lot, if we choose between investment alternatives. There is a trade-off between them: assets with higher risk (undesired) will provide higher returns (desired)… Sharpe ratio A simple measure that provides information on how much the = reward-to-variability additional return “costs” in terms of risk. It gives you the additional ratio return the market has paid for an additional unit of standard deviation. risk premium Sharp ratio = SD of the excess return Sharp ratio: the price of the risk or the reward to variability, a premium that you earn for taking risk. Risks may be due to volatility but it can also be a default risk or something… *Risk premium = return of the risk-free asset – return that you earned NOTE: the sharpe ratio is a meaningful performance measure only for an investor’s whole portfolio, whereas you should not use it for evaluating particular assets that you want to add to your portfolio. Gedownload door: hannahducatteeuw | [email protected] Wil jij6€76 per Dit document is auteursrechtelijk beschermd, het verspreiden van dit document is strafbaar. maand verdienen?