Introduction: what money isHave you ever wondered what money is? Many people confuse money with value, but money is neither gold nor a piece of paper. [1]Money is nothing more than an item of extreme liquidity, thanks to a social construction (or social pact). A highly liquid asset is one that can be exchanged quickly without a significant loss of value. Imagine the two situations below:Selling an item worth 100 reais (the Brazilian currency, R$) for 50 two-real notes;Selling an item worth 100 reais for 50 pencil cases worth 2 reais each.In theory there is no loss of value in either, but why does the second one sound so strange? You would hardly manage to exchange those pencil cases for another item worth 100 reais (maybe for one worth 20 or 30). That is why we prefer the piece of paper: it is accepted everywhere. This ease of exchange is what we call liquidity.What makes money money, then, is not the value it carries (everything in life has some value) but its liquidity. And, thinking more deeply, the value of money is not even the one printed on it: a R$ 100.00 note today will not buy the same items a year from now.“Money continuously changes in value”- Leon, your teacherThink about how many items you could buy with a 100-real note 10 years ago and how many you can buy now!“One of the basic premises of financial mathematics is that we cannot compare cash flows in different time periods”- Your teacher againFollowing this reasoning, R$ 100.00 today will not be worth the same a year from now, for several reasons. The first of them is the loss of purchasing power over time, which we call inflation.In practice, this means that to buy the same quantity of goods in the future, we will need more money than today.Inflation: where it comes fromInflation is a persistent and widespread rise in the prices of goods and services. Two main forces cause it: costs and demand.On the cost side are price increases in so-called basic inputs, such as electricity and fuel. These items push up the costs of every company and end up partly passed on to the final consumer when the product reaches the shelves of stores and supermarkets.On the other side there is demand-pull inflation. Demand comes from consumption (by households and the government) and from business investment. The economy's productive capacity is given by its stock of machines, factories, infrastructure, workforce and workforce skills, and in the short run these are hard to change. So when demand grows very fast, it outstrips supply, and this mismatch pushes prices up.Low and stable inflation is considered normal by the market. The problem arises when it grows: major distortions appear in the economy, such as the loss of purchasing power of wages that are not adjusted, losses for people living on fixed income, and uncertainty that leads companies to invest less. That is why Brazil runs an inflation-targeting system, measured by the IPCA (see below).To measure inflation, and thus understand the time value of money, we use price indices.If prices rise 25% over a period, how much purchasing power does money lose?Answer: 20% — what cost 100 now costs 125, so 100 reais now buy 100/125 = 0.8 of the basket, that is, 20% less. The 25% is the rise in prices, not the loss of purchasing power: the two rates only coincide when they are very small.Price indicesConsider a product that has price P₀ at time 0 and price Pₜ at time t. The price index between the two dates is:\[ P_{0,t} = \frac{P_t}{P_0}\]And the percentage change in price is:\[ j = P_{0,t} - 1 \]ExampleAt the beginning of September of a certain year, the price of a product was R$ 30.00 and, at the beginning of October of the same year, R$ 31.00. What is the price index of this product between the two dates? What is the percentage change?\[ \text{price index: }P_{0,t} = \frac{P_t}{P_0} = \frac{31}{30} = 1.0333... \]\[ \text{percentage change: }j = P_{0,t} -1 = 1.0333... -1 = 3.33\%\]A product cost R$ 40.00 and now costs R$ 46.00. What are the price index and the percentage change?Answer: Index 1.15 and change of 15% — 46/40 = 1.15, and the change is 1.15 - 1 = 0.15 = 15%. The index 0.87 comes from inverting the fraction (40/46); 115% confuses the index with the change.Cumulative rateInflation, like other indicators, changes its rate every month. To find the rate for a longer period, we can use the price index for the whole period or combine the rates of the shorter periods that make it up. For example, the quarterly rate comes from the rates of the first, second and third months of the quarter.The following relation holds (rates are multiplied, not added):\[ i_{\text{quarterly rate}} = (1 + i_{\text{first month rate}})(1 + i_{\text{second month rate}})(1 + i_{\text{third month rate}}) - 1 \]ExamplesIn two successive years, a certain product rose 10% and 12%, respectively. What is the cumulative rate of increase for the period?\[ i_{\text{two-year rate}} = (1 + 0.1)(1 + 0.12) - 1 = 0.232 = 23.2\% \]Notice that the cumulative rate (23.2%) is higher than the simple sum (22%): the second year's increase applies to a price that had already risen.In January, February, March and April of a certain year, the price of a product rose, respectively, 1.2%, 1.5%, 0.6% and 0.7%. What is the cumulative rate of increase for the four-month period?\[ i_{\text{four-month rate}} = (1 + 0.012)(1 + 0.015)(1 + 0.006)(1 + 0.007) - 1 = 0.0406 = 4.06\% \]Inflation was 1% in each of three consecutive months. What is the cumulative inflation for the quarter?Answer: 3.03% — 1.01 × 1.01 × 1.01 = 1.030301, that is, 3.03%. Adding the rates (3.00%) ignores that each month applies to prices already raised in the previous month.Brazil's main price indices: the measures of inflationAn aggregate price index, called a measure of inflation, tracks the prices of a predefined basket of goods and services. Each item enters with a weight that reflects how much households spend on it; at IBGE (the Brazilian Institute of Geography and Statistics, the national statistics office), these weights come from the Household Budget Survey (POF). A very simple hypothetical basket would be, for example, 2 kg of rice and 1 kg of beans.The inflation rate for a month is the percentage change in the average price of this basket in that month compared with the previous month. Each index differs from the others in who calculates it, which basket it tracks (of which households or which sector) and in which period it collects prices.Broad Producer Price Index (IPA)Calculated by the Getulio Vargas Foundation (FGV IBRE), it tracks the prices of hundreds of products in transactions between companies, before they reach retail. Until 2010 it was called the Wholesale Price Index (Índice de Preços por Atacado), the name behind the acronym IPA. In 1964, when monetary correction (inflation indexation) was introduced in Brazil, the IPA was chosen as the reference index for adjusting the Readjustable National Treasury Bonds (ORTN). [2]Consumer Price Index (IPC) and Cost of Living Index (ICV)These indices measure changes in the prices of the goods and services consumed by households with well-defined characteristics. [3] The best known are FGV's IPC (households earning 1 to 33 minimum wages, in several state capitals), the IPC-Fipe (city of São Paulo, households earning 1 to 10 minimum wages) and DIEESE's ICV (city of São Paulo).National Construction Cost Index (INCC)Also calculated by FGV, it is a monthly index that tracks the prices of materials, services and labor in civil construction. It measures the evolution of the sector's costs, one of the thermometers of the level of economic activity, and is widely used to adjust installments on properties bought before completion. [4]General Price Index (IGP) and IGP-MThe IGP was designed by FGV in the late 1940s to be a broad measure of price movements, covering not only different activities but also distinct stages of the production process. That is why it is a weighted average of the three indices above: IPA (60%), IPC (30%) and INCC (10%). The large weight of the IPA makes the IGP react strongly to the exchange rate and to commodity prices.The IGP has three versions that differ only in the price-collection period: the IGP-M (from the 21st of the previous month to the 20th of the reference month), the IGP-DI (from the first to the last day of the month) and the IGP-10 (from the 11th to the 10th). The IGP-M is traditionally used in Brazil to adjust rental contracts and some public utility rates.General Real Estate Market Index – Commercial (IGMI-C)The IGMI-C does not measure inflation: it is a return index for the Brazilian commercial real estate market, calculated by FGV IBRE and published quarterly. Its goal is to portray, as comprehensively as possible, the price appreciation and income (rents) of properties such as offices, shopping malls, hotels and warehouses throughout Brazil.National Consumer Price Index (INPC) and Broad National Consumer Price Index (IPCA)Both are calculated by IBGE through the National System of Consumer Price Indices (SNIPC), which continuously collects prices at commercial and service establishments, public utility companies and households (for rent and condominium fees), in the urban areas of several metropolitan regions and capitals. What changes between them is the basket, that is, the households whose consumption is tracked.The INPC was created to guide wage adjustments. Its target population is households earning 1 to 5 minimum wages whose reference person is a wage earner, living in the urban areas surveyed. [5]The IPCA covers households earning 1 to 40 minimum wages, whatever the source of income, living in the urban areas surveyed — a range that covers about 90% of the households in those areas. Being the broadest, it is Brazil's official inflation index: since 1999 it has been the measure used by the inflation-targeting system. The target set by the National Monetary Council (CMN) has been, since 2025, a continuous target of 3% per year, with a tolerance of 1.5 percentage points either way. [6]IBGE also produces versions of the IPCA for specific purposes: the IPCA-15, with collection from roughly the 16th of one month to the 15th of the next, released as a preview of the month's inflation, and the IPCA-E, which is the IPCA-15 accumulated each quarter. Other indices were published by IBGE in the past: Consumer Price Index – IPC (March 1986 to February 1991); Tax Value Adjustment Index – IRVF (June 1990 to January 1991); Basic Basket Index – ICB (August 1990 to January 1991); Minimum Wage Adjustment Index – IRSM (January 1992 to June 1994); Special National Consumer Price Index – INPC-E (November 1992 to June 1994); and Consumer Price Index series r – IPC-r (July 1994 to June 1995).ExampleSuppose that, in the base month, the average price of a basket is R$ 500.00 and, in the following months, R$ 510.00, R$ 520.00 and R$ 540.00. Find the inflation rate for each month.\[ i_{1} = \frac{510}{500} - 1 = 0.02 = 2\% \]\[ i_{2} = \frac{520}{510} - 1 = 1.96\% \]\[ i_{3} = \frac{540}{520} - 1 = 3.85\% \]Each rate is calculated relative to the immediately preceding month, not to the base month. Cumulative inflation over the three months is 540/500 - 1 = 8%, the same result as 1.02 × 1.0196 × 1.0385 - 1.Which index is used to check whether Brazil met its inflation target?Answer: IPCA, from IBGE — it has been the official index of the targeting system since 1999, because it covers households earning 1 to 40 minimum wages, about 90% of urban households. The INPC is also from IBGE, but tracks only households earning 1 to 5 minimum wages whose reference person is a wage earner; the IGP-M is from FGV and is used mainly for rents.In the IGP-M, which component has the largest weight?Answer: IPA, at 60% — the IGP is the weighted average of IPA (60%), IPC (30%) and INCC (10%). That is why the IGP-M can drift far from the IPCA when the dollar or commodities rise: most of it measures producer prices, not consumer prices.Exercises1. In January, the average price of a basket was R$ 150.00 and, in February, R$ 153.00. What was the inflation rate for February?2. In August of a certain year, the price of a product rose 2% and, in September of the same year, 3%. What is the cumulative rate of increase for the two-month period?3. In January, February and March of a certain year, the inflation rates were, respectively, 1.6%, 0.76% and 0.92%. What is the cumulative inflation rate for the quarter?4. In four consecutive months, the price of a product rose 2%, 2.6%, 3.1% and 1.2%. What is the cumulative rate of increase for the four-month period?5. In a two-month period, cumulative inflation was 1.8%; in the first month, the rate was 0.5%. What was the inflation rate in the second month?6. Cumulative inflation over five months was 4%. What must the inflation rate be in the sixth month for the cumulative rate for the half-year to be 5%?7. If the inflation rate is 0.7% in each of six consecutive months, what is the cumulative rate for the half-year?8. If, from January to December of a certain year (January and December included), the monthly inflation rate is 0.87%, what is the cumulative inflation rate for the year?9. Suppose that, in four consecutive months, the price of a stock fell 5% per month. What is the cumulative decline over the four-month period?10. If, in June, the price of a stock rises 20% and, in July of the same year, falls 20%, what is the cumulative rate for the two-month period?Answer key1. 2%2. 5.06%3. 3.31%4. 9.19%5. 1.29%6. 0.96%7. 4.27%8. 10.95%9. −18.55% (a decline of 18.55%)10. −4%References[1] https://financaspessoais.organizze.com.br/o-que-e-e-o-que-nao-e-dinheiro/[2] http://portalibre.fgv.br/main.jsp?lumPageId=402880811D8E34B9011D984D9EE23590[3] https://www.dieese.org.br/analiseicv/icv.html[4] http://portalibre.fgv.br/main.jsp?lumChannelId=402880811D8E34B9011D92B7684C11DF[5] http://www.portalbrasil.net/inpc.htm[6] http://www.portalbrasil.net/ipca.htm[7] http://portalibre.fgv.br/main.jsp?lumChannelId=4028818B33F047B80133F53367111455
ردود الفعل
0
0 تعليقات
كن أول من يعلق
لا شيء هنا بعد.