1 5 Volatility in the Overnight Money-Market Rate Allan Bødskov Andersen, Economics INTRODUCTION AND SUMMARY This article analyses the day-to-day fluctuations in the Danish overnight money-market rate during the period from January 999 to 3 May 004. The fluctuations in the Danish overnight rate may seem relatively large compared with the overnight rate in the euro area (Eonia). However, direct comparisons are difficult to make because both Eonia and the Danish overnight rate are affected by various technical factors. In the euro area, the overnight rate is influenced by the ECB s monthly reserve maintenance period, while the corresponding Danish rate is impacted on the days when Danmarks Nationalbank conducts open market operations. Fluctuations in the overnight rates are also due to normal variations in supply and demand in the money market. In other words, there is nothing unnatural about a certain amount of volatility in the overnight rate. In its weekly open market operations, Danmarks Nationalbank determines the 4-day rate. Under normal market conditions, the currentaccount rate moreover sets a lower limit for the overnight rate, as current-account deposits with Danmarks Nationalbank are always a riskfree alternative to money-market placements. As explained below, these monetary-policy instruments create volatility in the overnight rate. The analysis shows that this technical variation in the overnight rate explains a significant amount of the overall variation, namely approximately 50 per cent. Another source of money-market volatility is expectations of changes in the official interest rates. During the period under review, this type of volatility in the Danish overnight rate has been limited to a few, but rather significant fluctuations. These are most obvious in Chart as the The overnight rate in the euro area and its relation to the ECB s monetary-policy instruments are described in detail in The Monetary Policy of the ECB, European Central Bank, 004, and will not be discussed further in this article.
2 6 OVERNIGHT RATES IN DENMARK AND THE EURO AREA Chart Per cent Danish overnight rate Euro-area overnight rate Note: Overnight rates for Denmark and the euro area (Eonia) are used. Source: Danmarks Nationalbank. three "peaks" following the interest-rate reductions at the end of 00 and during the first half of 003. The background to the fluctuations is relatively straightforward, cf. below. Adjusted for the few episodes with large fluctuations as a consequence of expectations of changes in the official interest rates, almost 80 per cent of the overall variation in the overnight rate can be attributed to technical factors. As the overnight volatility is thus mainly of a technical nature, it is unproblematic from a monetary-policy viewpoint. The money-market participants understand the workings of the overnight market, and the volatility in the overnight rate does not affect the money-market rates further along the yield curve, cf. Chart. The analysis of the remaining non-technical variation, reflecting general supply and demand effects, shows that volatility trends during the period under review are time-varying and persistent both of which are classic features of financial time series. Moreover, there is a tendency for some correlation between the overall development in volatility and Danmarks Nationalbank s internal spread, defined as the lending rate less the current-account rate. On the other hand, there seems to be no systematic impact from changes in the official interest rates on the volatility of the overnight money-market rate. This analysis is conducted within the framework of a generalised, autoregressive conditional heteroskedasticity model (GARCH).
3 7 MONEY-MARKET RATES WITH DIFFERENT MATURITIES Chart Per cent Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Overnight 4 days month 3 months Note: The Chart shows daily observations for the period July 003 to May 004. Source: Danmarks Nationalbank. TECHNICAL VOLATILITY IN THE OVERNIGHT RATE The Danish money market is the market for interbank loan agreements and interest-rate derivatives with a maturity of up to one year. The overnight rate is the rate that players in the Danish money market pay or receive when they respectively borrow or lend liquidity from one banking day to the next, for instance from today to tomorrow or from Friday to Monday. Interaction with the monetary-policy instruments The Danish money market is affected by the monetary-policy instruments used by Danmarks Nationalbank. The development in the overnight rate is closely linked to Danmarks Nationalbank s lending rate and the certificate-of-deposit rate. Danmarks Nationalbank offers sale of certificates of deposit and enters into monetary-policy loan agreements in the course of the regular open market operations on the last banking day of the week, i.e. usually on Fridays, and when warranted by forecasts of central-government receipts and disbursements. 3 Apart from 3 For a description of the Danish money market, see Chapter of Monetary Policy in Denmark, Danmarks Nationalbank, nd edition 003. Danmarks Nationalbank s monetary-policy instruments are described in Chapter of Monetary Policy in Denmark, nd edition 003. The overall liquidity is affected by Danmarks Nationalbank s foreign-exchange interventions and payments to and from the central government. Danmarks Nationalbank prepares forecasts of the daily liquidity impact of the central government s payments and notifies the money-market participants in advance of when it offers sale or buy-back of certificates of deposit.
4 8 these operations, Danmarks Nationalbank conducts operations without prior announcement when required, for instance in connection with unexpected shifts in central-government payments. Certificates of deposit and monetary-policy loans have a maturity of 4 days. The certificate-of-deposit rate and Danmarks Nationalbank s lending rate are normally identical. In addition to buying certificates of deposit, the monetary-policy counterparties may also place liquidity as demand deposits in current accounts at Danmarks Nationalbank. The rate of interest on these deposits is lower than the certificate-of-deposit rate. Since June 003, the current-account rate has been per cent p.a., while the certificateof-deposit rate has been.5 per cent p.a. The example below illustrates how the monetary-policy instruments affect the overnight money-market rate. The example is based on a typical situation in which Danmarks Nationalbank offers sale of certificates of deposit and monetary-policy loans on a Friday, while the next announced open market operation is on the following Friday. A monetary-policy counterparty then has the following options for placement of liquidity in the coming seven-day period: placement in the money market at the current overnight rate for each of the seven days, or purchase of certificates of deposit at Danmarks Nationalbank, accruing interest at.5 per cent for seven days. The overnight rate is marketdetermined and will adjust in the following seven days so that the overall return on placement in the overnight market more or less matches the alternative placement in certificates of deposit. On the face of it the overnight rate in an equilibrium could adjust to approximately.5 per cent on Fridays and on each of the following four banking days (Monday-Thursday). However, on the banking days Monday-Thursday, the alternative placement to the overnight rate is not the certificate-of-deposit rate, as no open market operations are conducted on these days, but rather current-account deposits with Danmarks Nationalbank. For these the interest rate, as stated, is lower than the certificate-of-deposit rate, in the example per cent. If the overnight rate was, say,.5 per cent on these banking days, the monetary-policy counterparties would seek to achieve this higher return by The relevant time horizon is seven days, although the duration of certificates of deposit and monetary-policy loans is two weeks the reason being that the interest rates on certificates of deposit and monetary-policy lending are normally identical. In the absence of expectations of changes in official interest rates, the monetary-policy counterparties will, on days of open market operations, be able to reconsider their net placement of liquidity with Danmarks Nationalbank without taking their previous decision into account. In practice, the two returns will not match completely. As deposits with Danmarks Nationalbank are risk-free, a risk premium will apply to placement in the money market, cf. Box, p. 3. This factor is accounted for in the following analysis.
5 9 lending in the overnight market, rather than placing liquidity in current accounts. Other things being equal, this will increase the supply of liquidity in the overnight market and drive down the interest rate towards the current-account rate. On banking days without open market operations, the spread between the overnight rate and the currentaccount rate will reflect the liquidity situation in the money market, together with a risk premium, as current-account deposits are always a risk-free option. For illustrative purposes, it is assumed that the overnight rate on the banking days Monday-Thursday is per cent. In other words, risk premia are disregarded. In order to comply with the requirement that the overall return on placement in the overnight market over a seven-day period must match.5 per cent, the overnight rate on Fridays must adjust to a level higher than.5 per cent. This is known as the "Friday effect" on the overnight money-market rate. In the example, we can calculate the "theoretical" overnight rate on Fridays (called r) on the basis of the following condition: () r per cent for three days + per cent for four days =.5 per cent for seven days. Note that "overnight" transactions concluded on a Friday run until the following Monday. Therefore, the overnight rate r on Fridays applies for three days. In the example, the overnight rate on Fridays must be.35 per cent to match the return on the alternative placement with Danmarks Nationalbank. Obviously, the "Friday effect" is seen not only on Fridays, but, in principle, on all days of open market operations. The effect is stronger, the longer the interval until the next announced open market operation, and the shorter the period that the overnight rate applies on days of open market operations. Chart 3 illustrates the effect for the period from July 003 until May 004. As will appear, the overnight rate is, on average, higher on days of open market operations and tends to peak on these days. However, the connection is not clear-cut as rather high overnight rates are sometimes also seen on days without open market operations. A cap applies, however, to the overall current-account deposits of the monetary-policy counterparties. However, the overall current-account limit has been fixed at a level high enough not to be restrictive in the daily settlement of payments. This aspect will therefore not be considered further in this article, but reference is made to the description of the current-account-limit system in Chapter of Monetary Policy in Denmark, Danmarks Nationalbank, nd edition 003. The displayed equation is simplified, as compound interest is not included in the seven-day placement in the money market. In practice, the compound interest is, however, very small on account of the short time frame.
6 30 THE OVERNIGHT RATE AND OPEN MARKET OPERATIONS Chart 3 Per cent Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Overnight rate Open market operation Note: Squares denote observations on days of open market operations. Source: Danmarks Nationalbank. Analysis of technical volatility A simple regression analysis is conducted of daily observations of the overnight rate during the period January 999 to May 004, a total of,353 observations, in order to examine the proportion of the overall variation in the overnight rate that is attributable to the Friday effect. The focus is on analysing the spread between the overnight rate and the current-account rate, below referred to as the r spread. An artificially high degree of explanation resulting solely from the fact that the overall trend of the level of the overnight rate is determined by the currentaccount rate is thereby avoided. It is sought to explain the interest-rate spread by the variable "Feffect", which assumes the value of 0 on days without open market operations. On days of open market operations, the variable assumes a value equal to the theoretical spread, allowing for the Friday effect as illustrated above. This means that the theoretical overnight rate is calculated based on equation (), subtracting the current-account rate. The calculations take account of the risk premium required by the money-market counterparties for placement in the money market, The calculation is made on days of announced as well as unannounced open market operations. The return required for the overnight placement is always calculated up to the next announced open market operation.
7 3 RISK PREMIA IN THE OVERNIGHT RATE Box Except for a few special cases, the overnight rate is consistently slightly above the theoretical lower limit set by the current-account rate. This is apparent from e.g. Chart 3 where the overnight rate is slightly higher than the current-account rate of.00 per cent throughout the period under review. This is because, as opposed to deposits with Danmarks Nationalbank (current-account deposits/certificates of deposit), placement of funds in the overnight money market for several days is not without risk, as the return on the placement is not known for certain in advance. Therefore, market participants require a risk premium as compensation for the risk of placing liquidity in the overnight money market. Various risk factors exist, such as: Random fluctuations in the overall liquidity in the financial sector mean that the return is subject to some uncertainty, given that on days of tighter overall liquidity, the overnight rate will, other things being equal, adjust to a higher level. The overall liquidity in the sector is affected, in particular, by central-government receipts and disbursements. These payments cannot be completely accurately predicted. The overall liquidity in the sector is also affected by Danmarks Nationalbank s foreignexchange interventions. The size and timing of Danmarks Nationalbank s interventions depend on the actual current conditions in the foreign-exchange market and thus cannot be predicted. Uncertainty as to the concentration of the overall liquidity and its distribution among various counterparties. When liquidity is concentrated in a few financial institutions, this may affect the overnight rate. Uncertainty as to the timing of unannounced open market operations. Uncertainty as to possible changes in official interest rates. Credit risk, on the other hand, does not seem to play any significant role as, for example, the 4-day money-market rates are usually not above the certificate-of-deposit rate, cf. also Chart. By way of comparison, the average overnight rate for the period illustrated in Chart (July 003 to May 004) was.7 per cent, or slightly above the certificate-of-deposit rate (.5 per cent) and the current-account deposit rate (.00 per cent) in the period, as a consequence of the Friday effect and risk premia. rather than as risk-free deposits with Danmarks Nationalbank. Box describes in more detail what the risk premium may be assumed to cover. The internal spread, "intspread", is also included as an explanatory variable. In practice, this is done by assuming that the risk premium is constant and equal to the average difference between the overnight rate and the current-account rate. This risk premium is then added to the return required for placement in the money market. While this approach ensures simple calculations, it obviously gives only a rough description of the risk preferences of the market participants. The internal spread is included in order to capture the effect of an increasing incentive to purchase certificates of deposit rather than placing funds in current accounts as the internal spread widens. Other things being equal, liquidity in the overnight market will thus decrease as the internal spread widens, which will have an upward impact on the spread between the overnight rate and the current-account rate.
8 3 The result of the regression: spread t t t t = (0.04) (0.034) () r = Feffect intspread + ε R While the variables are highly significant, the Friday effect has by far the strongest explanatory power. If the regression is based solely on this effect, the goodness of fit is 0.5. Thus, the Friday effect alone may explain half of the overall variation in the spread between the overnight rate and the current-account rate. The coefficient to the Friday effect is 0.63, implying that the overnight rate on average rises by 0.63 percentage point when the theoretical measure from equation () points to an increase of percentage point. This reflects that the overnight rate on days of open market operations is not determined solely by the Friday effect. The effect of expectations of changes in the official interest rates As Chart shows, there are marked peaks in the overnight rate, corresponding to December 00, 8 February/3 March 003 and June 003. On these days, the money market was influenced by strong expectations that the ECB (and thus Danmarks Nationalbank) would lower interest rates in the period until the next open market operation. Such expectations significantly magnify the Friday effect, as the overnight rate is expected to fall towards the middle of the period when the official interest rates (and thus the current-account rate) are expected to be lowered. Similarly, there is one very low observation of the overnight rate on 8 September 000. In this case, expectations of an increase in interest rates in the wake of the euro referendum drove down the overnight rate. The reason is that certificates of deposit are not attractive when the current-account rate is expected to rise before the maturity of the certificate. This increases the supply of liquidity in the money market, and pushes down the interest rate. If dummy variables are used to exclude these few instances of a strong impact from expectations of changes in the official interest rates, the goodness of fit rises to 0.78, while the parameter estimates for the other explanatory variables, cf. equation (), change only marginally. In other words, very few observations contribute significantly to the overall variation in the overnight rate in the period under review. Robust standard deviations are denoted in parenthesis.
9 33 MARKET-DETERMINED VOLATILITY IN THE OVERNIGHT RATE The part of the variation in the overnight rate that cannot be explained by technical volatility, i.e. just under 0 per cent, as described above, is analysed within the framework of a GARCH (Generalised AutoRegressive Conditional Heteroskedasticity) model. The precise specification of the model is described in the Appendix. The premise of the GARCH model is that periods of (conditional) volatility tend to "cluster", so that a period of relatively high volatility is followed by a period of relatively low volatility, and vice versa. This phenomenon is common for financial time series, and GARCH is a way to describe this structure. The rationale for applying the model to this case can be found in Chart 4, which shows the squared residuals from the regression analysis above. As appears, large residuals tend to be followed by other large residuals, while relatively small residuals, on the other hand, tend to be followed by other minor residuals. In this case, the model is used to give a picture of the marketdetermined volatility in the overnight rate. This volatility reflects the supply and demand situation for liquidity in the money market, as well as risk factors as described in Box. The development of the estimated volatility is shown in Chart 5 in which days of interest-rate increases and reductions during the period are specified separately. Volatility clearly varies strongly over time and also develops very persistently, cf. the Appendix. Visually assessed, there are no immediate indications that changes in the official interest rates as such have any systematic impact on volatility. However, the trend of the volatility level seems to depend positively on the internal spread, cf. Chart 6. As already stated, the wider the internal spread, the greater the incentive for the banks to purchase certificates of deposit. Other things being equal, this entails less overall liquidity in the money market. This, in turn, seems to increase the marketdetermined volatility of the overnight rate. The internal spread is also high when there are signs of unrest in the foreign-exchange market, which may in itself lead to more volatile rates. In practice, this is equivalent to the GARCH model being specified for the residuals from the regression analysis of the overnight rate above. Given the parameters of the model, the GARCH model provides an estimate of the current volatility for each observation, based on historical observations. The structure can be compared with an ordinary autoregressive model for the mean in which the current observation may be estimated based on historical observations.
10 34 SQUARED RESIDUALS Chart Note: The residuals for the regression model () including dummy variables. Source: Own calculations. MARKET-DETERMINED VOLATILITY Chart 5 Per cent Conditional volatility Interest-rate increase Interest-rate reduction Note: Squares and triangles denote days of interest-rate increases and reductions, respectively. Source: Own calculations.
11 35 MARKET-DETERMINED VOLATILITY AND INTERNAL SPREAD Chart 6 Per cent 35 Per cent Conditional volatility Internal spread Volatility trend line 0.00 Note: The trend line is a fitted polynomial. Source: Own calculations. CONCLUSION The overnight money-market rate is significantly affected by the interaction with the monetary-policy instruments used by Danmarks Nationalbank. In order to make placement in the overnight market attractive relative to placement with Danmarks Nationalbank, the overnight rate must rise on the days when Danmarks Nationalbank conducts open market operations. The analysis shows that this technical volatility in the overnight rate may explain a large part of the movement. There is no sign of any spill over effects on the interest rates further along the yield curve, making the variation in the overnight rate unproblematic from a monetary-policy viewpoint. The analysis of the market-determined element of the movements in the overnight rate shows that the volatility is strongly time-dependent and develops sluggishly. Overall, the volatility seems to correlate with the internal spread of Danmarks Nationalbank. This may be due to the fact that with a wider internal spread, there is, other things being equal, more incentive to purchase certificates of deposit and thus to tie up liquidity for 4 days. This results in less liquidity in the overnight money market, resulting in more volatile interest rates.
12 36 APPENDIX: THE GARCH MODEL The variation of the GARCH technique applied is an asymmetric GARCH(,)-in-mean with marginal t-distributed innovations. The specification used is spread t r = φ0 + φ Feffectt + φ intspreadt + φ3 log(ht ) + u u t = ε t h, ε t t t(ν) = α + α (u κ) + β h. ht 0 t t t φ 0, φ and φ correspond to the parameters of the ordinary regression analysis and capture the Friday effect. h t denotes the conditional variance. Inclusion of log(h t ) in the mean allows the conditional volatility to affect the overnight rate and is meant to capture any time-varying risk premium. The parameter κ captures any asymmetry in the GARCH volatility: if κ is, for example, negative, a positive shock to the overnight rate (u positive) will imply a higher conditional volatility relative to a negative shock of the same numerical magnitude. The model is estimated using maximum likelihood under the restrictions of α 0 >0, α +β >0 and α +β <. 3 The result is shown in Table A. THE GARCH MODEL Table A Mean Variance φ 0 φ φ φ 3 α 0 α β ν κ 0.34 (0.038) 0.67 (0.0) (0.06) 0.05 (0.0) (0.047).34 (0.) 0. (0.0) Note: Robust standard deviations are shown in parenthesis. Restrictions are binding. Source: Own calculations. All variables in the model are significant. The explanatory contribution from the internal spread has declined due to the high correlation between the internal spread and the conditional volatility, cf. also Chart 6, so that log(h t ) assumes some of the explanatory power from the internal spread. For the mean, the parameter for the Friday effect is, reassur- 3 The t-distribution is used because the current distribution for the interest rate has thicker tails than the normal distribution. The number of degrees of freedom ν for the marginal t-distribution is estimated in line with the other parameters of the model. Where ν is large, e.g. larger than 50 or 00, t(ν) is close to the normal distribution. For further details, see e.g. James D. Hamilton, Time Series Analysis, Princeton University Press, 994. Moreover, the dummy variables for the mean value are included as described in the article. The first two restrictions ensure that the conditional variance is positive. The third restriction ensures stationary volatility and finite unconditional variance of the overnight rate, as any integrated GARCH volatility is difficult to interpret in the current application.
13 ingly, almost unchanged relative to the simple regression analysis. The parameter for the conditional volatility (φ 3 ) indicates that a higher conditional volatility, on average, leads to a significant widening of the spread between the overnight and the current-account rates. This is in harmony with an interpretation of log(h t ) as a time-varying risk premium. As far as the variance is concerned, it should be noted that α +β is very close to, as the restriction is binding. This indicates that the conditional volatility moves very persistently. The number of degrees of freedom ν in the t-distribution is estimated at approximately.3, describing a distribution with significantly thicker tails than the normal distribution. This is a typical phenomenon for financial time series. With a starting value of h 0 for the conditional variance and given the model s parameters, h t is calculated recursively for all time points t from the equation above. As starting value, the unconditional variance for the spread between the overnight and the current-account rates is used. The conditional volatility is then given as the square root of h t and reproduced in Charts 5 and 6. 37
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