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The Definite Guide to Products Updates Rici Total Return Index Certificates Q1 07

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the cell OS is calculate and interpret.the value price return and total return.of an index index definition and.calculations of value and returns a.security market index represents a given.security market market segment or asset.class most indices are constructed as.portfolios of marketable securities.price return index only reflects changes.in market prices of constituent.securities the value of a price return.index is calculated as the following so.here you have the formula the value of a.price return index in the numerator we.can see it's the sum n I is the number.of units of constituent securities held.in the index portfolio and P I is the.unit price of the Constituent security.and D equals the value of the divisor.the divisor is a number initially chosen.and inception.it is frequently chosen so that the.price index has a convenient initial.value such as 1000 for a security market.index price return can be calculated in.two ways either the percentage change in.value of the price return index or the.weighted average of price returns of the.Constituent securities that's fairly.important to understand but you'll have.a better understanding of that as we go.through quite a few calculations with.regards to this through not only this.but some following l OS as well I've.always found that the best way to.understand these calculations with.regards to the indices is to just jump.in and do a bunch of calculations and.then it becomes quite clear what's.happening so let's look at this practice.question an analyst gathers the.following information for a price.weighted index comprised of securities.ABCDEF and GHI so we have the beginning.of period price the end of period price.and the total dividends okay so ABC has.a beginning period price of 25 ending.period 27 dividend a 1 d EF beginning.period price 35 pounds end of period.price 25 pounds in total dividends of 1.pound fifty and GHI beginning price.fifteen pounds ending price sixteen.total dividends.one pound so the question is asking for.the price return of the index is it a.negative four point six percent B.negative nine point three percent or C.negative thirteen point nine percent.okay I realize we're tackling some.questions fairly early in this process.with regards to these L OS and later on.there's another l OS which is calculated.and analyzed the value in return of an.index given its weighting methods so.we're going to see more but nevertheless.I wanted to put this up front right away.to show you the importance of how it's.very it's really important in reading.these questions because in this case.it's saying it is a price weighted index.and we're being asked to calculate the.price return so it's really important.when we're doing our calculations that.were reading the questions carefully and.we're seeing what the method is for.calculating the index okay so we can see.in this case when it's a price weighted.index and we're calculating the price.return it's fairly simple we don't need.the dividends at all in this case so.that's there as red-herring information.we would need that if we were.calculating the total return but in this.case it's a price weighted index and.we're calculating the price return so.all we need to do is we add up the.beginning price and here I've put it in.bold and green there's three securities.one two three we add up the prices and.sum them that's with regards to the.formula we have a sum of 75 we have the.ending period price of 68 so to.calculate the return it's just 68 minus.75 divided by 75 minus nine point three.three percent so the correct answer is B.okay quickly we can also I know some.folks like to calculate it as just 68.divided by 75 minus one times 100 and.we're gonna get the negative nine point.three three okay okay as I said this is.a little bit early in the process to be.doing these type of calculations but I.just wanted to stress very early as you.get into the reading and into the alos.for this section.that it's just the importance of reading.the question and seeing what we're doing.here because in this next question an.analyst is gathering the following.information but it's for an equal.weighted index comprised of assets a b.and c and again it's calculating for the.price return okay.so again they're giving us the beginning.period price the ending period price and.the total dividends and you can see for.a the beginning price is 10 euros ending.price 12 euros total dividends 0.75 be.the beginning price 20 euros ending of.period price 19 euros total dividends of.1 euro and for C the beginning price 30.euros ending price 30 euros and the.total dividends is 2 euros so the price.return of the index is a 1.7 percent B 5.percent or C 11.4% okay you can see in.this case that they're giving the.information with the regards to an equal.weighted index it's not a price weighted.index okay and so the answer the correct.answer is B it's five percent and I want.to show you that a lot of people if they.don't read the question carefully this.is why I'm putting this up front with.regards to this reading in these LSE's.if you just looked at the beginning.prices and ending prices I don't even.really need my calculator here 30 plus.20 50 that's 60 okay and here I have my.ending prices 30 plus 19 plus 12 just.bring up the calculator very quickly I.can do 30 plus 19 plus 12 and that's.going to give us 61 okay and if I was.calculating as the price return for a.price weighted as I did in the previous.question I would do 61 divided by 60.okay - 1 and then times by the 100 and.that you can see indeed aha.I would answer a but a is not correct.it's not correct why and this is why I.put this early you need to read the.question very carefully this is an equal.weighted index.so the price can be calculated as the.weighted average of the price returns of.the Constituent securities okay again in.this case it's asking for the price.return so we don't need the dividends.that is given there as a red herring.information but what I do need to do is.I need to calculate the returns of each.of the securities price returns so you.can see for a 12 divided by 10 minus 1.times 100 or this way 12 minus 10.divided by 10 ending - beginning /.beginning we're going to get 20% here.okay that's the return on a 4b the.return is 19 minus 20 divided by 20.that's a minus 5% okay and finally for C.there's no return ok 30 minus 3 divided.by 30 is zero so what we needed to do.then is we're going to add these up and.you can see we're gonna have a 15% okay.and we're gonna divide by 3 because it's.equally weighted and we're gonna get 5%.so the price return index assigns a.weight of one-third to each asset.because it's equally weighted therefore.the price return is one-third times 20%.minus 5% plus zero okay so I put those.two questions very early in the process.don't worry there's going to be lots.more practice but I just wanted to show.very quickly and very early the real.importance of reading these questions.very carefully so continuing with index.definition and calculations of values.and returns now we're going to look at.total return total return measures price.appreciation plus interest dividends and.other distributions thus the total.return of an index is the price.appreciation or change in the value of.price return index plus income which is.dividends and/or interest over the.period expressed as a percentage of the.beginning value of the price return.index so here we can see we've got the.formula the total return and this is.easy by the end of the cfa level one you.really know it's ending minus beginning.plus the income divided by the beginning.okay so there's no worries in.calculating the total return and the.total return.an index can also be calculated as the.weighted average of the total returns of.the constituent securities that's.important to know and the calculation of.index values over multiple time periods.requires geometrically linking the.series of the index returns okay so if I.have here the value of the index at at.the beginning period on for the ending.period I'm just going to be multiplying.the value of the beginning times 1 plus.1 plus the period return times 1 plus.the period return and you know if it was.for 3 periods 1 plus the period return.and we've studied that in the quants.before how we calculate the geometric.returns so I'm just jumping into the.e-book here very quickly I just want to.show you the calculation of index values.over multiple time periods because my.handwriting was not so clear on that.previous slide perhaps I just want to.show you the calculation of index values.over multiple time periods requires.geometrically linking this series of.index returns we've studied this before.in the quant that's why we do as a.foundation and then it comes up in terms.of different applications and this is.one of them ok so I just wanted to spend.a quick second because this is you know.it could very easily get a question that.given the level of the index at the.beginning and a series of returns.calculate the value of the index at the.end of the period ok so you can see.there's the formula which we which I had.talked about and you can see that this.is the value of the price return index.at given time T which would be the.ending and it's the the value of the.price return index at the inception.times 1 plus the period return so it.just gives another little example here.you can see at time 0 the index is at.1,000 okay so of course we're starting.with 1,000 and then I have a 5% return.in period 1 and a 3% return in period 2.so this is just to get to the ending.value this is really easy just start.with your beginning 1000 and it's going.to be times 1.05 times 1.0 3 and we're.gonna have an ending value of 1000 81.5.okay so that's really easy and we see.lots of practice questions where you.need to use that.formula just going to finish this LS.with one last practice question but now.we're going to look at the calculation.for the total return so again this is.giving us the same data as the previous.question and analyst gathers the.following information for an equal.weighted index comprised of a B and C so.we've got the beginning prices the.ending prices and the total dividends in.this case it's asking for the total.return of the index so again we're going.to need those dividends this time and.the total return of the index is a 5% B.7.9 percent or C 11.4% okay this is a.nice little practice question to end on.so again it was asking for the equal.weighted index so step one we're gonna.calculate the returns total returns for.each which you can see is ending -.beginning plus the dividends divided by.the beginning so we should know that.this is ending - beginning plus the.dividends divided by the beginning okay.for each one and so we calculate for a.the return total return is twenty seven.point five percent for B the total.return is zero percent and for C the.total return is six point seven percent.so then again an equal weighted index.applies the same weight one third to.each Securities returns therefore the.total return we're going to add the.three together twenty seven point five.plus zero plus six point seven and.divide by three we're going to get.eleven point four percent so the correct.answer is C okay nice little question to.end this L OS on don't worry we're going.to be doing lots more calculations later.with another LS in terms of calculating.returns of given the weighting of a of.an index calculating the returns and.that's the last slide for this LS thank.you.

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