Real Interest Rate Impact On Investment And Growth - Reserve Bank Of India

1y ago
6 Views
1 Downloads
814.85 KB
43 Pages
Last View : 24d ago
Last Download : 3m ago
Upload by : Audrey Hope
Transcription

Real Interest Rate impact on Investment and Growth –What the Empirical Evidence for India Suggests? 1AbstractMonetary policy is often expected to adopt a pro-growth stance in a phase of prolongedslowdown in growth and sluggish investment activities. Sacrificing inflation, i.e. loweringnominal policy rate even when inflation persists at a high level, is a convenient means tolower real interest rates, which in turn could be seen as a pro-growth stance of monetarypolicy. This paper, using both firm-level and macroeconomic data, and alternativemethodologies - such as panel regression, VAR, Quantile regression and simple OLS –finds that for 100 bps increase in real interest rate, investment rate may decline by about 50bps and GDP growth may moderate by about 20 bps. The empirically estimated sensitivity ofinvestment and growth to changes in real interest rate suggests that if the RBI can lower reallending rates, it can also stimulate growth. Review of literature highlights that a central bankcan lower real interest rates either through financial repression or by not respondingaggressively to inflation while raising the nominal policy rates in response to inflation.Empirical estimates for India indicate that RBI’s monetary policy response to inflation has notbeen aggressive, and as a result the Fisher effect –i.e. one for one response of interest rateto inflation that could leave the real rate constant – does not hold. Thus, even when a highnominal interest rate may often signal that monetary policy stance is tight, because of higherinflation and absence of Fisher effect, lower real interest rate may actually be growthsupportive. In India, real lending rates in recent years have been generally lower than thelevels seen during the high growth phase before the global crisis. But lower real rates in thepost-crisis period have coincided with sluggish investment and GDP growth. This is due tothe fact that while real rates are lower, marginal productivity of capital, or expected return onnew investment has also declined, which has dampened the expected positive impact oflower real rates on investment. In such a scenario, one policy option could be to lower realrates even more, by raising inflation tolerance, i.e. lowering nominal policy interest rate evenwhen high inflation persists or inflation expectations remain high. This paper, however,provides robust empirical justification against any policy of lowering policy interest rateswhen inflation persists above a threshold level of 6 per cent. The beneficial impact of lowerreal rates on growth that may be achieved through higher inflation tolerance is more thanoffset by the harmful effect of high inflation, particularly when it exceeds a threshold level of6 per cent.1This is an inter‐departmental study, prepared jointly by a group comprising Shri SitikanthaPattanaik, Dr. Harendra Behera and Shri Rajesh Kavediya from Monetary Policy Department(MPD), Dr. Abhiman Das and Dr. Arvind Kumar Shrivastava from Department of Statisticsand Information Management (DSIM) and Dr. Himanshu Joshi from Department of Economicand Policy Research (DEPR). The study was prepared under the guidance of Shri DeepakMohanty, Executive Director. The group benefited from extensive and useful commentsreceived from two anonymous referees and from participants during presentations of thestudy in a seminar of CFOs of corporates and banks, in the DEPR Annual ResearchConference, and in a seminar organised in ISI‐Kolkata. Views expressed in this paper areentirely personal.1

Real Interest Rate impact on Investment and Growth –What the Empirical Evidence for India Suggests?I. IntroductionThe Reserve Bank had to face and manage a difficult growth-inflation mix in 201213, with persistently high inflation requiring resolute anti-inflationary thrust in theconduct of monetary policy on the one hand, and sluggish growth impulseswarranting adequate and unambiguous monetary policy stimulus to spur growth onthe other. Facing this delicate growth-inflation balance, the Reserve Bank explicitlycommunicated that: (a) growth sacrifice is a necessary - though unpleasant - meansto contain demand side pressures on inflation, (b) high interest rate reflecting antiinflationary stance of monetary policy is only one of the factors behind the slowdownin growth, and (c) real interest rates, which could be more relevant than nominalinterest rate for influencing investment activities and overall economic growth, arelower now compared with the high growth phase before the global crisis, pointing tothe role of non-monetary factors in driving and sustaining the slowdown in growth.In terms of exact communication from the RBI on these aspects, the Mid QuarterReview (MQR) of Monetary Policy dated June 18 2012 highlighted that “. it isrelevant to assess as to what extent high interest rates are affecting economicgrowth. Estimates suggest that real effective bank lending interest rates, thoughpositive, remain comparatively lower than the levels seen during the high growthphase of 2003-08. This suggests that factors other than interest rates arecontributing more significantly to the growth slowdown.” Subsequently, in the firstquarter review (FQR) dated July 31, 2012, it was stressed that “.While monetaryactions over the past two years may have contributed to the growth slowdown – anunavoidable consequence – several other factors have played a significant role. Inthe current circumstances, lowering policy rates will only aggravate inflationaryimpulses without necessarily stimulating growth.” This paper was conceptualisedagainst this background, with the aim of empirically examining some of the puzzlingpolicy questions of direct relevance to monetary policy. The relevant questions formonetary policy include whether nominal or real interest rate matters for influencinginvestment and growth, and can a central bank influence real interest rates? Can alow nominal or real lending rate stimulate investment demand and growth, orwhether a supportive non-monetary environment is more important for growth? Ifsacrifice of the inflation objective is a means to lower real interest rates, can growthbe really stimulated through a lower real interest rate, particularly in an environmentwhere inflation is allowed to persist at above the threshold level? No single empiricalpaper can provide definite answers to all these complex, highly debatable, questions.This paper, however, makes an attempt to seek broad answers to these questions,based on analysis of available macro-economic and firm-level data, using alternative2

econometric methodologies. In the Third Quarter Review of monetary policy inJanuary 2013, while lowering the repo rate by 25 bps, it was communicated that theexpected outcome would include “.support growth by encouraging investment”. Therepeated emphasis in monetary policy statements during 2012-13 on the expectedrelationship between interest rate and investment activity and GDP growth providedthe key motivation for this paper. Against this context, the paper is organised into sixsections. Section-II sets out some of the theoretical controversies on real interestrate. A short review of empirical literature on sensitivity of investment and growth tochanges in real/nominal interest rates is presented in Section-III. Section-IV coverssome broad policy inferences that could be derived from a mere look at trends inrelevant data, besides a narration of the data used in the study. Empirical estimatesderived from use of four alternative methodologies – panel regression, quantileregression, ordinary least squares (OLS) regression and VAR – are analysed inSection-V. Feedback received from representatives of industry and commercialbanks during a discussion on the significance of nominal versus real interest ratefor investment planning is encapsulated in Section-VI. Concluding observations arepresented in Section-VII.Section-II: Controversies on Real Interest RateReal interest rate, being an unobservable variable, and also given that in manydifferent ways the real rate could at best only be approximated using alternativemeasures of both forward looking and backward looking inflation expectations,theoretical and empirical literature on the subject is replete with controversies.This section aims at presenting only those controversies which are relevant to thebroad theme of the paper, i.e. the impact of nominal versus real interest rate oninvestment and growth.Can a central bank change real interest rates?A central bank can change real interest rates in two different ways; first, throughfinancial repression/reforms, and second, through a monetary policy response toinflation in a manner that does not allow the Fisher effect to hold. Financialrepression could include measures such as regulated interest rates with explicitor implicit caps on nominal rates – irrespective of the level of inflation, directedlending – preventing cost of funds to reflect underlying risks, captive financing ofthe government borrowings – either through public ownership of banks orexcessive use of moral suasion or bank regulation, high reserve requirementsand securities transactions tax, and capital controls that prevent outflows ofdomestic savings and thereby help maintain low domestic interest rates.According to Reinhart (2012), for about 35 years after the end of World War-II,real interest rates in advanced economies remained highly depressed, reflectingfinancial repression. Then came the wave of financial liberalisation, and real ratesstarted rising, during 1981 to 2007. Since the global crisis, however, these3

economies are back to another phase of financial repression, with largemonetised financing of fiscal deficits, new forms of repression such as macroprudential measures, systemic risk regulation, and growing justification inintellectual debates for use of capital controls as a policy tool. In this third phasebetween 2008 and 2011, negative (or non-positive) real rates were observed inclose to half of the observations, and real rates were less than 1 per cent in about82 per cent of the observations (Table 1). Two important points to notice fromthis table are: (a) the third phase since the global crisis appears to be the mostrepressive, in terms of the levels of real interest rates, and this phase coincidedwith the great recession – not high growth, and (b) the second phase reflectscoexistence of both high real rates and high growth. Thus, sustained ultra-loosemonetary policy to deliver negative real rate as a means to spur growth is notalways effective, and, high real rates that may result when a country moves fromfinancial repression to reforms could actually deliver higher, not lower, growth.Besides financial repression/reforms, a central bank’s monetary policy responseto inflation can also influence real interest rates, and thereby investment andgrowth.Table 1: Real interest rates in advanced economies(shares of observations at or below)Real interest rate1945-19801981-2007 2008-2011 046.910.549.5 1 per cent61.625.282.1 2 per cent78.636.297.2 3 per cent88.655.099.5Source: Reinhart, April 2012 (real ex-post Treasury Bill rates).Can monetary policy change real interest rates?If investment is sensitive to changes in real rates, then for a central bank’smonetary policy to be effective, its changes in nominal rates should influence realrates. In other words, the direction of causation should be from nominal to realrates. Theoretical literature, however, suggests that real rate is a realphenomenon, and can be determined only by real factors. Given the real rate,depending on changing inflation expectations, nominal interest rate may change.Thus, the direction of causation is from inflation expectations to nominal rate, fora given real rate. The debate on nominal versus real rate, from the standpoint ofrole of monetary policy, however, offers different possibilities.Henry Thornton (1802) was possibly the first one to differentiate between market(money) rate of interest on lonable funds and expected yield on new capitalprojects (or real rate). According to his assessment:(a) inflation could be theresult of difference between money rate and real rate, and (b) inflationaryexpectations can create a wedge between the two. Thornton’s idea was4

reformulated, after about 100 years, by Knut Wicksell (1907) 2 , who alsoemphasised the difference between the “money rate (i)” and the “natural rate(R*)”. When these two rates are equal, desired savings (S) desired investment(I), aggregate demand aggregate supply, and hence there would be pricestability. However, when i R*, then I S, leading to credit/ money expansion, andhence inflation. What is particularly important to notice in this argument is thatneither money is an exogenous determinant of inflation nor the causation runsfrom higher prices to higher money growth. Instead, both prices and moneygrowth changes result in response to the difference between i and R*. Moreover,for the purpose of price stabilisation – knowledge of natural rate (R*) should notbe a constraint. The simple rule should be – if prices are rising, raise the moneyrate (i). Unless money rate (i) is lower than the natural rate (R*), prices should notrise. Hence adoption of the simple rule should ensure price stabilisation.The realised real rate is often presented in the form of an identity: r i – p – r*p,where r is real rate, i is nominal rate and p is inflation (realised/expected). Thecross-product part is often ignored at low inflation for policy analyses, but in ahigh inflation environment, the cross product could be significant. Irving Fisher(1936) 3 used the same formulation, i.e. i r p r*p, and also suggested limitingvalues (i.e. non-negative i), and most importantly, lagged adjustment of nominalrates to changes in inflation. Since nominal rates do not move exactly to offsetprice changes, realised (ex post) real rates do vary. That is, real rates are notconstant, unlike Fama’s (1975) empirical emphasis on constant real rates. Sincenominal rates do not respond one-for-one to changes in inflation: (a) realised realrates often move inversely in relation to nominal rates, (b) higher volatility is seenin real rates than in nominal rates, and (c) real rates often become negativeduring periods of high inflation (Mishkin, 1981 & 1984; Huizinga and Mishkin,1986).Thus, if monetary policy (i.e. higher nominal rate) responds to high inflationexpectations – one for one - then constant real rate should materialise (i.e.current nominal rate would then reflect only market expectations of futureinflation). However, if the response coefficient is less than one, real rate wouldchange. In other words, lack of full adjustment of nominal rate to inflation is thedriver of non-constant real rates. Summers (1982) suggested that both in the prewar and post war-periods, there is little evidence of nominal rate rising one-forone relative to increase in inflation. This he ascribed to possible money illusion infinancial markets, i.e. agents used to possibly ignore inflation in financialcalculations earlier, and over time, financial markets have become increasingly23Alfred Marshall (1890) was the first one to use the concepts of “real” and “nominal” rates.The Fisher Identity:Or,Commonly used,(1 rt) (1 it)/(1 πe(t 1))rt (it ‐ πe(t 1))/(1 πe(t 1) )rt (it ‐ πe(t 1))5

sensitive to inflation, but still not enough to remove money illusion completely.“.How unlikely is it that market participants should be unaware of the distinctionbetween nominal and real interest rates? It is noteworthy that it was not until the20th century that the distinction was even introduced into economic analysis.There is little evidence in mainstream economic writings in the l950's and 1960'sof an awareness of this distinction.” Chadha and Dimsdale (1999) also foundhigher sensitivity of nominal rates to inflation in the post-war period, mainly after1970s, which they ascribe to greater inflation focus of monetary policy; “.the lackof response of nominal interest rates to inflation in the early post-war years in allcountries.can be explained by the high priority given to output relative toinflation”. With increasing focus of central banks on inflation, and severalcountries adopting explicit inflation targeting, the interest rate response toinflation has also increased (Table 2). According to Friedman and Schwartz(1976), financial markets are also learning to better conform to the Fisher effect.An obvious consequence of lack of one-for-one response of nominal rate toinflation is the negative relationship between observed real rate and inflation.When inflation rises, nominal rates may not increase as much (reflecting inflationtolerance of central banks), leading to lower real rates. Similarly, when inflationdeclines nominal rates may not decline as much, thereby leaving the real rateshigher. The absence of Fisher effect, i.e. one-for-one change in nominal rate inresponse to change in inflation, is also evident in India (Table 3).Table 2: Low-to-high Fisher Effects:Regression Coefficients (short-term rates on inflation)CountryPre- WW .01Germany-0.040.01Source: Chadha and Dimsdale (1999)Post WW 1969-790.230.680.600.741980-970.770.890.690.966

Table 3: Weak evidence of Fisher Effect in India – a driver of non constant realrates?Time periodvariablesCoefficientt-stat1997Q3 2012Q1EFFECTIVE, WPIG0.621.74***1998Q1 2012Q1EFFECTIVE, WPIG0.491.72***1998Q1 2012Q1WPIG(-1), CALL0.442.14**2004Q2 2012Q1WPIG(-1), CALL0.513.14*EFFECTIVE: Effective Policy Rate; WPIG: WPI Inflation (y-o-y); CALL: Weighted average call rate. Allvariables are stationary (results in Appendix Table 1)*, **, ***: Significant at 1%, 5% and 10% level, respectively.When could a lower interest rate need not stimulate growth andinvestment?It is a fact that weighted average lending rates in India since the 2008 globalcrisis have been lower than the rates that prevailed during the high growth phasebefore the global crisis (Section-IV). The obvious question that arises then is – ifhigher rates did not impact growth adversely during the high growth phase, whyshould a lower rate be blamed for the slowdown in growth since the global crisis?This could be explained by comparing the level of interest rate with the marginalproductivity of capital at the macro level and internal rate of return (IRR) at thefirm level.At the macro-level, for policy purposes, two things are important: (a) sensitivity ofinvestment to changes in interest rate, and (b) how the interest rate comparesrelative to changing marginal efficiency of capital. In terms of standard Keynesiananalysis, the former could be explained through usual text book representation ofthe shape of the Marginal Efficiency of Investment (MEI) curve and the latterthrough the Marginal Efficiency of Capital (MEC) curve (Chart-1). The MEI curveshows sensitivity of investment to changes in interest rate. If the MEI curve is notvery sensitive in a country, then larger cuts in rates could be desirable, ifmonetary policy has to bear the burden of reviving investment and growth. But inreality, this sensitivity may be time varying. Even with near zero policy rate andmassive quantitative easing, advanced economies have not been able to revivedurable growth. That is because of sharper fall in MEC, as reflected in continuousbackward shifts in the MEC on account of depressed investment climate, intensedeleveraging, and depressed return expectations on new investment. Even inIndia, reflecting the contagion from sluggish global growth and domesticgovernance concerns, the MEC would have shifted down, and this continuousdownward drift cannot be prevented only with cuts in interest rate. For givenMEC, by the time interest rate is lowered to incentivise investment, MEC maydrop further, requiring a further cut in interest rate. In an environmentcharacterised by continuously downward drifting MEC, repeated cuts in interestrate would amount to chasing a falling MEC, which at some point may become7

effective only if the factors driving the downward drift in MEC stop or reverse. Ifthe factors causing the downward drift in MEC do not reverse, then repeated cutsin interest rate would amount to wasting the monetary policy space, and couldbecome particularly dangerous in an environment characterised by persistentlyelevated risks to inflation.Chart-1: MEI and MEC – how much interest rate should drop to promote investment?At the firm level, why a lower interest rate may not stimulate investment needs tobe assessed by comparing the interest rate with internal rate of return (IRR). Fora new investment project, what matters is the interest rate relative to IRR. If aparticular amount of borrowed money (C) is used to acquire a capital good, whichin turn is expected to yield a flow of return over say three years (of R1, R2 andR3), then the simple identity would yield the internal rate of return (r):C [R1/(1 r)] [R2/(1 r)2] [R3/(1 r)3]The IRR is that rate of discount, which would equate discounted present value ofexpected return over three years to the cost of the project, making NPV (netpresent value) of the project equal to zero. If the interest rate [or the hurdle ratewhich is equal to the weighted average cost of capital (WAAC) plus risk premia]is lower than the IRR, the NPV of the project would be positive, therebyencouraging new investment. Thus, as long as interest rate is lower than IRR,additional investment will continue. In a period of economic slowdown, progrowth monetary policy may push the interest rate down; but if the IRR also falls,and that too at a faster rate due to lower expected return on investment, thendespite the support of a pro-growth monetary policy stance, IRR may remainbelow the interest rate, and thereby defeat the policy objective of promotinggrowth and investment through a lower interest rate. Thus, lower interest ratealone is not an indicator of pro-growth stance of policy. It should be seen relativeto IRR. In a high growth phase, because of bullish expected return on investment,8

IRR may be higher, and therefore, a higher interest rate may still facilitateinvestment and growth. During a phase of economic slowdown, however, notonly that the IRR falls, but the hurdle rate may also rise - despite lower policyinterest rates – due to higher risk premium added to WAAC.It is possible that, an increase in interest rate may also change the returnprospects (i.e. R1, R2 and R3 may decline), which in turn will change (depress)the IRR. As a result, the pace of additional investment will slowdown. For theinvestment cycle, by how much return prospects change because of interest ratechanges on the one hand and non-monetary factors on the other becomeimportant. For example, in an overheating phase of the business cycle, despitehigh interest rate, buoyant return prospects may prompt additional investment.Whereas in a slowdown phase, a lower interest rate alone may not improvereturn prospects, and need not trigger a fast recovery.Extending such firm specific relationships to the level of the overall economy maycreate scope for ambiguities, particularly because investment horizons ofdifferent firms are different, and long-term interest rate expectations of differentfirms may be quite divergent. Using any single measure of interest rate to studythe impact on investment demand, thus, would always have its own limitations.But monetary policy decisions have to be always based on macro-levelinteractions among key economic variables, and differential impact acrosssectors should not undermine the relevance of macro level relationships forconduct of policy. Notwithstanding the importance of sector specific polices toaddress sector specific concerns, for monetary policy, what matters is thetransmission of policy rate changes to effective borrowing costs, and an averagerepresentative measure of effective cost of borrowing should provide usefulevidence on the sensitivity of investment demand to interest rates in theeconomy. This paper, in Section-V, aims at estimating sensitivity of investmentdemand and GDP growth to changes in interest rate, using both aggregatemacro-level data as well as sector level data.In terms of simple explanation of the dilemma for monetary policy, it is importantto recognise the distinction between movement along an investment demandcurve, and shifts in the investment demand curve. A change in interest rate canat best help in influencing movement along the investment demand curve, giventhe degree of sensitivity (elasticity) of demand to changes in interest rates. Theintended impact on investment demand may fail to materialise if non-monetaryfactors trigger a shift in the investment demand curve that works exactly in theopposition direction.Which interest rate matters for investment – Real or Nominal?While planning a new investment project, invariably it is the nominal interest ratewhich will go into project evaluation, but implicitly, inflation will also be part of theassessment of expected cash flows, which will be discounted to the present using9

the nominal interest rate to arrive at the net present value (NPV) of the project.Thus, even if explicitly a firm may not use real interest rate, implicitly it takes intoaccount its own effective real interest rate, depending on its own inflationexpectations as part of cash flow projections, and effective nominal cost ofcapital. For each firm, the duration of the project and hence the term period ofborrowings as also the firm’s credit worthiness will together influence the firmspecific borrowing costs (with firm specific term premium and risk premium) andthe inflation expectations implicit in cash flows could also be quite different fromother firms. For the economy as a whole, however, aggregate measures ofeffective cost of borrowings and inflation expectations could help in inferring theoverall relationship between real cost of funds and investment trends. It is notthat firms will behave similarly to similar levels of real rates at the macro level,when relevant nominal rates and inflation expectations are quite different acrossfirms. For example a 3 per cent real rate could coexist with 5 per cent nominalrate and 2 per cent inflation and also 15 per cent nominal rate 12 per centinflation. But high inflation itself may operate as an independent drag oninvestment, even if the real rate remains unchanged. This point comes to the foreclearly in the empirical estimates for India presented in Section-V.Real interest rate – always a real phenomenon?If monetary policy response to inflation can influence real rates, at least in theshort-run, what happens to the argument then that real rate is a real – not amonetary phenomenon? Real rate changes should reflect thrift and productivity,the typical neo-classical view, that remains very much relevant in the long-run.Empirical literature also suggests that endogenously determined shifts in realinterest rates could be explained by observed historical events, such as oil priceshocks, large fiscal imbalances, stock market crash, and major tax reforms; “.itis still inconclusive whether monetary policy has had any effects on the realinterest rate” (Manopimoke, 2008). Emphasising the role of nonmonetary factorsin determining real rates, Allospp and Glyn (1999) noted that “.savings,population growth and technology determine the equilibrium, steady state,capital-to-output ratio and marginal product of capital, i.e. the interest rate.”Higher real rates, thus, could be the result of faster population growth,technological progress or lower savings.Keynes (1936) was the first one to suggest explicitly that (nominal) interest rate isa monetary phenomenon, determined by the interaction between money demandand supply - contrary to the prevailing consensus till that time - and that the realeconomy should adjust to nominal interest rates, not the reverse.As per the standard Keynesian analysis, interest rate is determined by theinteraction of demand for money and supply of money. Exogenous moneysupply, which is determined by a central bank, will set the interest rate in thesystem for given money demand. Is the interest rate then a purely monetaryphenomenon? The answer would be no, because even in the Keynesiansystem of macro-dynamics, the level of income is a determinant of interest rate10

through money demand, which in turn is also influenced by the interest rate.Interest rate relative to marginal efficiency of capital influences the investmentdemand, and given the multiplier - for given propensity to save - income level isinfluenced. The dynamic interaction, thus, suggests that interest rate may bedetermined by the interactions between money demand and money supply, butinterest rate itself can influence money demand, through the influence oninvestment demand.Oscar Lange’s representation of the same dynamics assumes somewhat morerealistic possibilities. Unlike Keynes, consumption is viewed as a function of bothincome and interest rate, and investment a function of both consumption demandand interest rate. Since both consumption and investment demand could bepartly credit financed, and because that consumption demand can influenceinvestment demand, this specification has been used more often in empiricalresearch on the subject.The Keynesian prescription had to face stiff resistance from the super-neutralityproposition, that suggested neutrality of money- or inability of money to influencereal variables - in both short-run and long-run. In the subsequent period, a thirdview on interest rate evolved (the classical lonabale funds theory and Keynes’liquidity preference theory being the first two), which is the horizontalist viewpropounded by Moore (1988). According to this, money is endogenous (unlikeKeynes’s exogenous

If investment is sensitive to changes in real rates, then for a central bank's monetary policy to be effective, its changes in nominal rates should influence real rates. In other words, the direction of causation should be from nominal to real rates. Theoretical literature, however, suggests that real rate is a real

Related Documents:

while, the difference between the ex ante real interest rate—the nominal interest rate minus expected infla-tion—and the equilibrium real interest rate is defined as the real interest rate gap. In the new Keynesian model, the real interest rate (RIR hereafter) gap is central to the determination of output and inflation.

changes on the exchange rate. However, changes on exchange rate cause changes in the local interest rate while changes on the foreign interest rates do not cause changes in the local interest rate. In addition, changes on both the exchange rate and foreign interest rate jointly do cause changes on the local interest rate. Finally changes on

interest rate. An interest rate future is actively used to hedge against future interest rate movement, i.e., so-called interest rate market risk. Due to the varying feature of the underlying interest rates, the way to calculate the price and to quote the interest rate future varies a lot.

3 A Functional Time Series Approach 16 . interest rate at which payments are made based on a notional amount. The price of an interest rate derivative depends on the level of the interest rate and its expected change in the future. To price an interest rate derivative, a common approach is to de ne the future evolution of the interest rates .

Interest rate (§ 230.2(o)) An interest rate is the annual rate of interest paid on an account and does not reflect compounding. For purposes of the account disclosures in section 230.4(b)(1)(i), the interest rate may, but need not, be referred to as the "annual percentage rate" in addition to being referred to as the "interest rate."

Lecture Notes: Interest Rate Theory Foreword Goals I Basic concepts of stochastic modeling in interest rate theory. I "No arbitrage"as concept and through examples. I Concepts of interest rate theory like yield, forward rate curve, short rate. I Spot measure, forward measures, swap measures and Black's formula. I Short rate models I A ne LIBOR models I Fundamentals of the SABR model

The theory of compound interest handles this problem by assuming that the interest earned is automatically reinvested. With compound interest the total investment of principal and interest earned to date is kept invested at all times. A constant rate of compound interest implies a constant effective rate of interest, and, moreover, that .

Semi-Annual When interested is compounded semiannually (twice per year), you must DIVIDE the interest rate by the number of interest periods, which is 2. 6% annual interest rate 2 interest periods 3% semiannual interest rate To find the number of payment periods, multiply the nu