Latest workings

How do select market rates affect the FHLB advance rates?

 

 

A look at how market swaps, libor, US treasury and federal funds interest rates affect the bullet advance rates from the Federal Home Loan Bank of Boston.

 

 

Introduction

 

In the turmoil of the current economy, it is beneficial to have an ability to forecast and predict what the wholesale funding rates that the bank can borrow at.  This analysis pulls together Federal Home Loan Bank of Boston bullet advance rates and its affect from movements with swap rates, libor rates, treasuries, and Fed Funds rates.  The goal was to find the correlation between all these rates, and how the FHLB puts together its advance rates.  On the Federal Home Loan Bank of Dallas, Texas website, it states that bullet advance rates for 1 year or less are based on 1 year libor. For terms greater than 1 year, the bullet advance rates are based on swap rates.  Understanding the effect of different market rates on the FHLB rates is important for the management of funding and interest rate risk exposure. 

 

 

Data

 

In preparing the regression, correlation and spread analyses, it was found that daily data produced more precise equations, as opposed to monthly data.  Terms used were 1 year, 3 year, 5 year, 7 year and 10 year.  For the FHLB rates, data was pulled directly from the FHLB Boston website.  I took data from August 1st, 2007 through July 31st, 2008 to gather a full year of data.  Data for swaps and Federal Funds rates were pulled from Bloomberg terminal within the same range.  I found the data for historical treasury rates from the US treasury website. For the spread analyses, each variable was subtracted from the FHLB rates, and then the absolute average for the spread analyses. 

 

Table 1 through 5 shows the descriptive statistics for each variable by term (1 year, 3 year, 5 year, 7 year or 10 year).  For each table, the first row shows the statistics for the FHLB.  It looks like the mean for each term increases significantly by about 30 basis points.  This means that as the term lengthens, on average it is more expensive to borrow from the FHLB.  The same is said for swap rates and treasuries, although not as big of jumps between terms. Fed Funds do not have a “term” rate, and therefore remain the same in each table.  With the Fed Funds, it would be more appropriate to look at the median, rather than the mean, as the rates do not vary often, and they remain at quarter rates (e.g. 5.25, 4.75, 2.25).  It is interesting to look at the standard deviation of each rate.  For example, in looking at 1 year for FHLB, 68% of the rates are within +/- 89 bps from the average, 3.60.

 

 

Table 1: Descriptive statistics for 1 year term

 

Term:

1 year

 

mean

median

st. dev

min

max

FHLB

3.60

3.29

0.89

2.12

5.20

Swaps

3.65

3.29

0.96

2.11

5.25

LIBOR

3.78

3.48

0.95

2.18

5.28

Treasuries

2.86

2.51

0.99

1.32

4.89

Fed Funds

3.46

3.00

1.25

2.00

5.25

 

Table 2: Descriptive statistics for 3 year term

 

Term:

3 year

 

mean

median

st. dev

min

max

FHLB

3.95

3.97

0.65

2.76

5.21

Swaps

3.88

3.89

0.71

2.47

5.16

Treasuries

3.03

2.93

0.80

1.52

4.64

Fed Funds

3.46

3.00

1.25

2.00

5.25

 

Table 3: Descriptive statistics for 5 year term

 

Term:

5 year

 

mean

median

st. dev

min

max

FHLB

4.32

4.34

0.51

3.20

5.34

Swaps

4.21

4.23

0.57

3.10

5.29

Treasuries

3.42

3.35

0.62

2.23

4.69

Fed Funds

3.46

3.00

1.25

2.00

5.25

 

Table 4: Descriptive statistics for 7 year term

 

Term:

7 year

 

mean

median

st. dev

min

max

FHLB

4.64

4.67

0.42

3.61

5.47

Swaps

4.46

4.45

0.47

3.50

5.42

Treasuries

3.69

3.63

0.51

2.71

4.75

Fed Funds

3.46

3.00

1.25

2.00

5.25

 

Table 5: Descriptive statistics for 10 year term

 

Term:

10 year

 

mean

median

st. dev

min

max

FHLB

4.93

4.93

0.33

4.03

5.62

Swaps

4.70

4.68

0.45

1.25

5.54

Treasuries

4.05

3.99

0.38

3.34

4.84

Fed Funds

3.46

3.00

1.25

2.00

5.25

 

 

Empirical Results

 

There were seven different specifications that were estimated.  The dependent variable for each specification was the FHLB rates, measured in percentage points.  Swaps, libor rate (for 1 year term only), treasuries and Fed Funds were the independent variables.  Table 6 below shows the results of each equation.  The 1 year and the 7 year term was estimated twice, with the 1 year versus libor only, and the 7 year without the treasuries variable, as with it included the t-statistic and p-value shows that it is an insignificant variable.  

 

Table 6: Regression results

 

 

 

Dependent Variable: FHLB (by terms)

 

1 year

1 year vs LIBOR

3 year

5 year

7 year

7 year w/o treasuries

10 year

Intercept

0.1722

0.0080

0.7179

0.7827

0.5547

0.6212

1.2775

 

(0.025)

(0.018)

(0.054)

(0.059)

(0.094)

(0.062)

(0.084)

Swaps

0.3625

 

0.6521

0.6685

1.0153

0.9406

0.0833

 

(0.058)

 

(0.042)

(0.048)

(0.081)

(0.016)

(0.033)

LIBOR

0.4885

0.9577

 

 

 

 

 

 

(0.052)

(0.005)

 

 

 

 

 

Treasuries

0.1338

 

0.2476

0.2352

-0.0753

 

0.8481

 

(0.022)

 

(0.039)

(0.047)

(0.079)

 

(0.044)

Fed Funds

-0.0273

 

-0.0141

-0.0240

-0.0478

-0.0509

0.0521

 

(0.007)

 

(0.006)

(0.006)

(0.007)

(0.006)

(0.007)

 

 

 

 

 

 

 

 

R-squared

0.9959

0.9940

0.9864

0.9745

0.9505

0.9503

0.8993

adj R-squared

0.9958

 

0.9862

0.9742

0.9499

0.9499

0.8981

 

 

 

 

 

 

 

 

Number of observations for each term: 252

 

 

Standard errors in parentheses

 

 

 

 

All at a significance of 5%

 

 

 

 

 

In interpreting the analysis, below I have outlined regression equations for each equation that was done, for simplicity. 

 

1 year FHLB = 0.17 + 0.36 swaps + 0.49 libor + 0.13 treas – 0.03 fed funds

 

1 year FHLB #2 = 0.008 + 0.9577 libor

 

3 year FHLB = 0.72 + 0.65 swaps + 0.25 treas – 0.01 fed funds

 

5 year FHLB = 0.78 + 0.67 swaps + 0.24 treas – 0.02 fed funds

 

7 year FHLB = 0.5547 + 1.02 swaps – 0.08 treas – 0.05 fed funds

 

7 year FHLB #2 = 0.62 + 0.94 swaps – 0.05 fed funds

 

10 year FHLB = 1.28 + 0.08 swaps + 0.85 treas – 0.05 fed funds

 

In looking at the intercepts of each equation, after 1 year term, the 7 year term seems to start at a lower base rate than the other terms.  This may lead one to believe that 7 year term may be cheaper.  But in actuality, the variables, specifically the swaps variable, has more of an impact than it does on other terms.

 

1 year FHLB is mostly impacted by the libor rate.  When researching what impacts the 1 year rate, the Dallas FHLB states that the 1 year bullet advance rates are based on libor.  With terms 3 through 7 year, swaps has a greater impact on FHLB rates than the other variables.  The Dallas FHLB states that anything greater than the 1 year term is based on swaps rates.  Yet when looking at the 10 year FHLB equation, it has the greatest base rate, and it is also affected most by treasury rates.  

 

1 year FHLB:

 

Equation 1:

1 year FHLB = 0.17 + 0.36 swaps + 0.49 libor + 0.13 treas – 0.03 fed funds

 

Breakdown of Analysis:

  • Adjusted r2 = .996.  99.6% of variance in 1 year FHLB advances is explained by swaps, libor, treasury rates, and Fed Funds.
  • Correlation between FHLB and all other varables are > .5 (basis for statistical judgment), and therefore are highly correlated, meaning one variable does effect another (in this case, FHLB advance rates).
  • Dissecting the equation:
    • Base rate = 0.17% (if all variables were 0, then FHLB would still be at the base rate)
    • Swaps impact = For every percentage point increase in swaps, FHLB increases by .36%
    • Libor impact = For ever percentage point increase in libor, FHLB increases by .49%
    • Treasuries impact = for every percentage point increase in treasuries, FHLB increases by .13%
    • Fed Funds impact = for every percentage point increase in the Fed Funds rate, FHLB decreases by .03%.  Fed Funds has a mild inverse effect on FHLB rates.
  • In looking at this dissection, FHLB rates are more affected by swaps and libor than treasuries and Fed Funds by the fact that their coefficients/impact listed above are higher.
  • Spreads (average spread between FHLB and variable, in absolute value):
    • FHLB to swaps: .0080
    • FHLB to libor: .0294
    • FHLB to treasuries: .6301
    • FHLB to fed funds: .4280
  • These spreads show that FHLB rates are more closely in line with swaps and libor, with a larger spread between treasuries and fed funds.
  • The variance of these spreads (σ2) are as follows:
    • FHLB to swaps: .0077
    • FHLB to libor: .0066
    • FHLB to treasuries: .0338
    • FHLB to fed funds: .4010
  • In looking at the variance of the spreads, there are much smaller variances between FHLB to swaps and libor, than to Fed Funds.  It could be deduced that FHLB moves more in tandem with swap rates and libor than with Fed Funds in looking at this huge difference in variance.

 

Equation 2:

            1 year FHLB = 0.008 + 0.9577 libor

 

Breakdown of Analysis:

  • This equation was pulled out of the first equation based on the impact of libor on FHLB as stated above, and the statement on the Dallas FHLB’s website saying 1 year advance rates are based on libor.
  • r2 = 0.994.  99.4% of variance in 1 year FHLB advances is explained by the 1 year libor rate.
  • Correlation between FHLB and libor is .997, meaning these variables are highly correlated.
  • In dissecting the equation, the base rate = 0.004%.  With the impact of libor, for every percentage point increase in libor, FHLB increases 0.9577.
  • One may interpret this equation as nearly 1 for 1: every percentage point libor increases, FHLB increases about 1 percentage point.
  • Because of this close correlation between the two variables, it is necessary to analyze the spreads between the two.
  • The spread deviation from the mean = 0.055, with the variance of the spread = 0.003.  This tight variance shows that the regression line closely follows the actual points plotted.

 

3 year FHLB:

 

Equation:

3 year FHLB = 0.72 + 0.65 swaps + 0.25 treas – 0.01 fed funds

 

Breakdown of Analysis:

  • Adjusted r2 = .986.  98.6% of variance in 3 year FHLB advances is explained by swaps, treasury rates, and Fed Funds.
  • Correlation between FHLB and all other varables are > .5 (basis for statistical judgment), and therefore are highly correlated, meaning one variable does effect another (in this case, FHLB advance rates).
  • Dissecting the equation:
    • Base rate = 0.72% (if all variables were 0, then FHLB would still be at the base rate)
    • Swaps impact = For every percentage point increase in swaps, FHLB increases by .65%
    • Treasuries impact = for every percentage point increase in treasuries, FHLB increases by .25%
    • Fed Funds impact = for every percentage point increase in the Fed Funds rate, FHLB decreases by .01%.  Fed Funds has an insignificant inverse effect on FHLB rates.
  • In looking at this dissection, FHLB rates are more affected by swaps than treasuries and Fed Funds by the fact that their coefficients/impact listed above are higher.
  • Spreads (average spread between FHLB and variable, in absolute value):
    • FHLB to swaps: .0068
    • FHLB to treasuries: .9237
    • FHLB to fed funds: .4897
  • These spreads show that FHLB rates are more closely in line with swaps with a larger spread between treasuries and fed funds.
  • The variance of the spreads (σ2) are as follows:
    • FHLB to swaps: .0110
    • FHLB to treasuries: .0356
    • FHLB to fed funds: .5387
  • In looking at the variance of the spreads, there is a much smaller variance between FHLB to swaps and treasuries than to Fed Funds.  It could be deduced that FHLB moves more in tandem with swap rates and treasury rates than with Fed Funds in looking at this huge difference in variance.

 

5 year FHLB:

 

Equation:

5 year FHLB = 0.78 + 0.67 swaps + 0.24 treas – 0.02 fed funds

 

Breakdown of Analysis

  • Adjusted r2 = .972.  97.2% of variance in 5 year FHLB advances is explained by swaps, treasury rates, and Fed Funds.
  • Correlation between FHLB and all other varables are > .5 (basis for statistical judgment), and therefore are highly correlated, meaning one variable does effect another (in this case, FHLB advance rates).
  • Dissecting the equation:
    • Base rate = 0.78% (if all variables were 0, then FHLB would still be at the base rate)
    • Swaps impact = For every percentage point increase in swaps, FHLB increases by .67%
    • Treasuries impact = for every percentage point increase in treasuries, FHLB increases by .24%
    • Fed Funds impact = for every percentage point increase in the Fed Funds rate, FHLB decreases by .02%.  Fed Funds has an insignificant inverse effect on FHLB rates.
  • In looking at this dissection, FHLB rates are more affected by swaps than treasuries and Fed Funds by the fact that their coefficients/impact listed above are higher.
  • Spreads (average spread between FHLB and variable, in absolute value):
    • FHLB to swaps: .1154
    • FHLB to treasuries: .8998
    • FHLB to fed funds: .9637
  • These spreads show that FHLB rates are more closely in line with swaps with a larger spread between treasuries and fed funds.
  • The variance of the spreads (σ2) are as follows:
    • FHLB to swaps: .0119
    • FHLB to treasuries: .0275
    • FHLB to fed funds: .8292
  • In looking at the variance of the spreads, there is a much smaller variance between FHLB to swaps and treasuries than to Fed Funds.  It could be deduced that FHLB moves more in tandem with swap rates and treasury rates than with Fed Funds in looking at this huge difference in variance.

 

7 year FHLB:

 

Equation 1:

7 year FHLB = 0.5547 + 1.02 swaps – 0.08 treas – 0.05 fed funds

 

Breakdown of Analysis:

  • Adjusted r2 = .950.  95.0% of variance in 5 year FHLB advances is explained by swaps, treasury rates, and Fed Funds.
  • Correlation between FHLB and all other varables are > .5 (basis for statistical judgment), and therefore are highly correlated, meaning one variable does effect another (in this case, FHLB advance rates).
  • Dissecting the equation:
    • Base rate = 0.55% (if all variables were 0, then FHLB would still be at the base rate)
    • Swaps impact = For every percentage point increase in swaps, FHLB increases by 1.02%
    • Treasuries impact = for every percentage point increase in treasuries, FHLB decreases by .08%. Treasuries have an insignificant inverse effect on FHLB rates.
    • Fed Funds impact = for every percentage point increase in the Fed Funds rate, FHLB decreases by .05%.  Fed Funds has an insignificant inverse effect on FHLB rates.
  • In looking at this dissection, FHLB rates are more affected by swaps than treasuries and Fed Funds by the fact that their coefficients/impact listed above are higher.
  • Spreads (average spread between FHLB and variable, in absolute value):
    • FHLB to swaps: .1818
    • FHLB to treasuries: .9563
    • FHLB to fed funds: 1.2125
  • These spreads show that FHLB rates are more closely in line with swaps with a larger spread between treasuries and fed funds.
  • The variance of the spreads (σ2) are as follows:
    • FHLB to swaps: .0157
    • FHLB to treasuries: .0321
    • FHLB to fed funds: 1.1011
  • In looking at the variance of the spreads, there is a much smaller variance between FHLB to swaps and treasuries than to Fed Funds.  It could be deduced that FHLB moves more in tandem with swap rates and treasury rates than with Fed Funds in looking at this huge difference in variance.

 

Equation 2:

7 year FHLB #2 = 0.62 + 0.94 swaps – 0.05 fed funds

 

Breakdown of Analysis:

  • This equation was pulled out of the first equation based on the impact of swaps on FHLB as stated above, with the fact that the treasuries variable was deemed insignificant (t-statistic = -0.94, P-value = 0.35).
  • r2 = 0.950.  95.0% of variance in 7 year FHLB advances is explained by the regression equations
  • Correlation between FHLB and libor is .9680, meaning these variables are highly correlated.
  • In dissecting the equation, the base rate = 0.62%.  With the impact of swaps, for every percentage point increase in swaps, FHLB increases 0.94.  With Fed Funds, for every percentage point increase in the Fed Funds rate, FHLB decreases by .05%.  Fed Funds has an insignificant inverse effect on FHLB rates.
  • One may interpret this equation as nearly 1 for 1: every percentage point swaps increase, FHLB increases nearly 1 percentage point.
  • Because of this close correlation between the two variables, it is necessary to analyze the spreads between the two.
  • The spread deviation from the mean = 0.1229, with the variance of the spread = 0.0151.  This tight variance shows that the regression line closely follows the actual points plotted.

 

10 year FHLB:

 

Equation:

10 year FHLB = 1.28 + 0.08 swaps + 0.85 treas – 0.05 fed funds

 

Breakdown of Analysis:

  • Adjusted r2 = .898.  89.8% of variance in 5 year FHLB advances is explained by swaps, treasury rates, and Fed Funds.
  • Correlation between FHLB and all other varables are > .5 (basis for statistical judgment), and therefore are highly correlated, meaning one variable does effect another (in this case, FHLB advance rates).
  • Dissecting the equation:
    • Base rate = 1.28 % (if all variables were 0, then FHLB would still be at the base rate)
    • Swaps impact = For every percentage point increase in swaps, FHLB increases by .08%
    • Treasuries impact = for every percentage point increase in treasuries, FHLB increases by .85%.
    • Fed Funds impact = for every percentage point increase in the Fed Funds rate, FHLB decreases by .05%.  Fed Funds has an insignificant inverse effect on FHLB rates.
  • In looking at this dissection, FHLB rates are more affected by swaps than treasuries and Fed Funds by the fact that their coefficients/impact listed above are higher.
  • Spreads (average spread between FHLB and variable, in absolute value):
    • FHLB to swaps: .2136
    • FHLB to treasuries: .8729
    • FHLB to fed funds: 1.1061
  • These spreads show that FHLB rates are more closely in line with swaps with a larger spread between treasuries and fed funds.
  • The variance of the spreads (σ2) are as follows:
    • FHLB to swaps: .0164
    • FHLB to treasuries: .0183
    • FHLB to fed funds: 1.2234
  • In looking at the variance of the spreads, there is a much smaller variance between FHLB to swaps and treasuries than to Fed Funds.  It could be deduced that FHLB moves more in tandem with swap rates and treasury rates than with Fed Funds in looking at this huge difference in variance.

 

Conclusion

 

The analysis of this paper shows correlation between FHLB and other variables.  Specifically, for the 1 year FHLB rates, it looks as if it is closely tied with libor rates.  With 3 year, 5 year and 10 year FHLB rates, they look to be tied to swap rates.  And lastly, with the 7 year FHLB rates, they are closely correlated with 7 year US Treasury rates.  These findings confirm the notion that rates are based off of libor and swap rates, with the exception of the findings related to the 7 year FHLB rates.  It is also seen that as the terms increase, the spread variances increase as well.  This may be in relation to the FHLB interest rates increasing as the term increases, or that simply the spreads generally widen with the term increase.

 

It is surprising how closely these rates are correlated with the FHLB bullet advance rates, and with each other.  There is speculation of multicollinearity, yet when put in context for economic significance, all these rates should be correlated.  For example, a 3-year T-bill is not going to be 5.00% with Fed Funds at 1.25%, a spread of 3.75%.  Taking this into account, I decided not to adjust the regression equations when assessing the relationships.  Another possible error that this analysis might have experienced is the behavior of the Fed Funds rate.  Because the rates are targeted at a specific level, they do not move around freely as the other rates do.  To avoid this, I could have used the Fed Funds effective rate, or blocked off the analysis each time the rate changes to see how the change affects other rates.  Using the Fed Funds effective rate might have a greater impact on the regression equations, as well as may have had a higher correlation with FHLB rates.

 

One process that this analysis did not look into was the skewness of the spreads.  In scratching the surface, there was evidence of skewness, as most equations seemed positively skewed when calculated out initially.  Evaluating skewness would give color to analyzing spreads between rates.  For instance, for 10 year FHLB rates in comparison with swaps, it looks as if spreads have a few outliers passed +2σ.  Looking at where the population lies for each rate spread, one may be able to anticipate how big of a spread there will be given one of the independent variables.

 

Historical spreads could also be looked at, where data would go for longer than a year. Looking at historical spreads could give greater analysis to the trend, whether spreads for rates are tightening or widening.  This may give clues to how some monetary policies (Fed Funds rates) are affecting other rates throughout history. 

 

It is clear that there is a relationship between FHLB of Boston’s bullet advance rates versus swaps, libor, and treasuries.  Further research is needed, though, on evaluating the spreads between FHLB rates and the other variables.  Intercepts of each equation is also worth investigating: what they are based on, what the FHLB considers an interest premium, etc.  Lastly another FHLB analysis could be a sensitivity analysis, where one would look at the possibilities of when the FHLB would call a loan to be paid earlier during different rate environments. This initial research has stemmed numerous of other ideas to be explored.  Initial research has shown that not a lot of analyses have been done on the Federal Home Loan Bank, and it would be beneficial to explore this lender as a lot of banks use it strategically for interest rate risk management.

 


Leave a Reply