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BFC5926 Financial Institutions and Markets
Creation date：2024-08-24 15:45:17
Belonging category：金融Finance
Tag BFC5926
Financial Institutions and Markets
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BFC5926
Financial Institutions and Markets
Seminar 3:
Risk, interest rates & yields
Reading: Topic 3 Reading List
Learning objectives
• Understand utility, risk and return
• Understand what determines interest rates
• Explain and construct the term structure of
interest rates
• Define and contrast the term structure of
interest rate related theories: unbiased/pure
expectations; market segmentation; liquidity
premium.
2
Utility, risk, and return
3
Utility
• Utility measures the satisfaction people receive from
consuming a good or service.
• Different individuals typically obtain differing amounts
of utility from the same source.
• We would like to maximize expected utility.
4
Utility (cont.)
• We would like to maximize expected utility.
• Marginal utility: the additional utility gained from the
consumption of one additional unit of a good or
service.
• Once having reached a certain level of satisfaction,
one’s satisfaction from additional units may start slow
and then even decline – diminishing marginal utility.
5
Diminishing marginal utility
It would seem possible to reach a position of
decline or negative marginal utility
6
Diminishing marginal utility
7
Quantity
Utility
Risk preferences
• You are given the choice between two scenarios.
– In a guaranteed scenario, you will receive $50.
– In the uncertain scenario, you have a 50/50
chance of either receiving $100 or nothing.
• The expected payoff for both scenario is $50.
• Are expected utility the same? – It depends on risk
preference.
8
Risk preferences
• Risk averse: [u(0)+u(100)]/2 < u(50)
9
Utility


u(100)

u(50)




u(0)
0 50 100 $
 You have $50
 The extra utility
from + $50 to get to
$100 is smaller in
magnitude than the
utility reduction
from - $50 to get to
$0.
Risk preferences
• People’s attitudes toward risk varies with their utility.
• Most investors are risk-averse – this means they
prefer less risk to more risk.
• Some, however, may be risk-neutral or indifferent to
risk.
• Still others may be risk-seeking and actually prefer
more risk to less.
10
Risk and return preference
• As most people are risk averse, they will only take a
risk if they expect an adequate reward.
• For a given level of return, risk averse individuals prefer
investments with lower risk;
• For a given level of risk, risk averse individuals prefer
investments with higher return.
11
Risk and return preference (cont.)
• The more expected risk that risk averse individuals
assume, the higher should be their expected return.
• Through proper risk management, risk can be
reduced/minimized but it cannot (in most cases) be
completely eliminated.
12
Risk and return
• Measure of return: Expected value or mean
• Measure of risk: The scattering of the other
possibilities around the expected return
 variation of returns or standard deviation of
returns.
13
Risk and return (cont.)
• Measure of risk: variation of returns or
standard deviation of returns.
– Standard deviation is a measure of total risk.
– However, a person should not be rewarded for
bearing risk that could have been diversified away
by investing in different assets
– Beta (non-diversifiable/ systematic risk) is a better
measure of risk.
14
Calculating return
• Historical average return:
= 1 + + ⋯

• Expected return is the weighted average of
all possible returns :
( ) = ( × )



15
Calculating risks
16
Determinants of
Interest Rates
17
Basis points & interest rates
• Interest rates (IRs) are expressed as percentages,
but those changes less than 1.00% are referred to
as basis points (bpts).
• There are 100 basis points in one per cent.
• For example, the Reserve Bank typically adjusts its
target cash rate by moves of 0.25% or 25 basis
points.
18
Determinants of interest rates
• The interest rate is the price of money and it reflects
the simple equilibrium between the supply and
demand for funds within a specific market.
• An increase in demand for credit will cause interest
rates to rise while a decrease should see interest
rates decline.
• Similarly, an increase (decrease) in supply of funds
will cause interest rates to fall (rise).
19
Further determinants
• What actually determines this supply and demand
for money has been the subject of considerable
research.
• These can be divided into:
– overall factors that impact on all rates
• such as overall economic growth, inflation, overseas
rates etc.
– instrument specific factors.
• such as issuer’s credit risk, liquidity risk of the
instrument, other instrument characteristics.
20
Overall determinants of IRs
• Government monetary policy
• Inflation (actual and expected)
• Overseas interest rates (FX rates)
• External current account and balance of
payments
21
Monetary policy
• Monetary policy involves setting the interest
rate on overnight loans in the money market
(‘the cash rate’).
• The cash rate influences other interest rates in
the economy, affecting the behaviour of
borrowers and lenders, economic activity and
ultimately the rate of inflation.
(Source: RBA website)
22
The Cash Rate
• The cash rate is the unsecured overnight
interbank lending rate.
• The cash rate is important because:
– It measures the return on the most liquid of
financial assets (bank reserves)
– It is integral to monetary policy
– It directly reflects the available reserves in the
banking system, which influences banks’
decisions on making loans.
23
RBA Official Cash Rate
24
Monetary policy objectives
• There are three main objectives that the RBA
tries to achieve with its monetary policy:
– The stability of the currency of Australia
– The maintenance of full employment in Australia
– The economic prosperity and welfare of the people
of Australia.
25
Inflation
• Inflation is the rate at which the general level of prices
for goods and services increase.
• Its direct effect on nominal interest rates is that it
erodes the real value or “purchasing power” of
financial assets
26
Inflation (cont.)
• Fisher Effect : (1 + i ) = ( 1 + r )( 1 +  )
where: i = nominal rate of interest
r = real rate of interest
 = expected inflation rate
often simplified to: i = r + 
• The indirect effect of increased inflation is that it may
signal an overheating of the economy.
27
Australian Consumer Price Inflation (CPI)
Source: Reserve Bank of Australia
28
Overseas rates
• Investors today look at returns in a global context.
If the risk & return benefits are better elsewhere,
they will move their money from one country to
another.
• This movement impacts on the local supply and
demand for money.
• It also has a major effect on foreign exchange rates.
29
Balance of payments
• Australia’s external accounts with the rest of the
world are reflected in its balance of payments &
external debt.
• While this impacts both on local foreign exchange
and interest rates, these factors have not been
considered as important as other factors by the
Reserve Bank of Australia in the past.
30
Term Structure of
Interest Rates
31
Term structure of interest rates
32
• Definition: The term structure of interest rates
expresses the relationship between interest rates and
different maturities.
• Also known as a yield curve.
• This structure assumes that everything else remains
the same.
• It is usually based on the relationship between
interest rates on zero-coupon bonds and the maturity
of those bonds.
• Long-term coupon bonds can be looked at as a series
of zero-coupon bonds with different maturities.
Zero coupon bonds
• A zero-coupon bond is
 a bond where the face value is repaid at the time of maturity, &
 an investor receives no interest (coupon) payments over the life
of the bond.
• The investor buys the zero-coupon bond by paying less than the
bond’s face or redemption value (FV).


= !
33
Zero coupon bonds (cont.)
• Why zero coupon bond is used?
 For yield curves, we need to remove all possible variations in
returns to keep the analysis simple.
With a coupon bond, the interest is paid regularly and then must
be reinvested – typically at different rates;
whereas a zero coupon has no reinvestment problems as there
are no payments!
34
Yield curves
• A yield is the total return from an investment.
• A yield curve depicts the relationship between
 the interest rates and,
most commonly, different debt maturities
 for a given borrower in a given currency.
• A more formal mathematical presentation of this
relationship is explained by the term structure of interest
rates.
35
Types of yield curves
• Upward sloping or normal
• Downward sloping or inverse
• Flat
• Humped - some combinations of the above
36
Time to maturity
Y
i
e
l
d
Humped Yield Curve
Upward sloping in practice
• A ‘normal’ yield curve is one in which longer maturity
bonds have a higher yield compared to shorter-term
bonds due to the risks associated with time.
• Historically, when yield curves steepen its slope, this
suggests improved economic growth.
• It is often seen at the start of economic expansion
periods,
because the expected growth will eventually force up interest
rates in the future.
37
Downward sloping in practice
• An inverse yield curve is one in which the shorter-term
yields are higher than the longer-term yields.
• Normally found when investors expect the economy to
deteriorate – a recession is expected.
• Long-term investors will accept reduced rates of longer
term interest rates now as they expect future long
term rates to decline further.
38
Flat yield curve in practice
• A flat yield curve means that the yield to maturity on
all debt instruments (for example, government
securities) is the same or very close to each other.
• This suggests that investors expect no specific change
in interest rates or rather there is no certainty on
future rates.
• In practice, it often foreshadows a slight decline in
rates.
39
Humped yield curves
• This is where the yield curve
1. either initially rises and then falls, or alternatively,
2. falls in the short term and then rises in the long term.
• This may also reflect some degree of uncertainty
about future rates
but reflects some preference for shorter rates in the first
case.
40
Australian Government Bond Yield Curve
41
Source: http://www.worldgovernmentbonds.com/country/australia/
Term Structure
Theories
42
Theories on term structure
• Three main theories that attempt to
explain term structure and its changes:
– Unbiased or pure expectations theory
– Market segmentation theory
– Liquidity premium theory
43
Pure expectations theory
• Suggest that the yield curve’s shape reflects the
market’s expectation of future interest rates.
• It assumes that financial instruments with different
durations are perfect substitutes.
• So, the yield on a long term security should be equal to
the expected geometric mean on a series of short term
instruments.
44
Pure expectations theory (cont.)
• So, the yield on a long term security should be equal to
the expected geometric mean on a series of short term
instruments.
• Geometric Mean Return (GM)
GM = [(1+R1)*(1+R2)*(1+R3)...(1+Rn)]1/n -1
45
Expectations theory
Explanation for the shape of yield curves:
– Inverse yield curve
Will result if the market expects future short-term rates
to be lower than current short-term rates
– Normal yield curve
Will result from expectations that future short-term
rates will be higher than current short-term rates
– Humped yield curve
Investors expect short-term rates to rise in the future
but to fall in subsequent periods
46
Expectations theory (cont.)
• Advantages:
– Explains why interest rate yields change over time.
– Explains why the interest rates on all securities tend to
move together rather than as separate sub-markets.
• Disadvantages:
– Cannot explain why yield curves usually slope upwards.
– It would suggest future short term rates are usually
expected to rise, but they are just as likely to fall.
47
Market segmentation theory
• The market is not one overall market but rather a
series of inter-connected markets.
 Financial instruments of different terms are
not substitutable.
• So, the supply and demand in each of these markets
determines the interest rate in each.
• They are then connected with each other in that
investors in one market will change their preferences
with sufficient compensation.
48
Term Structure & Market Segmentation
Maturity
Y
i
e
l
d
49
Note: the various Xs reflect different supply and demand curves for
securities for various maturity ranges
Segmentation in practice
• It is true that certain investors, particularly
institutional investors, have specific maturity
preferences due to their business.
• Commercial banks prefer shorter to medium term
securities due to the nature of their liabilities.
• Life insurance companies prefer longer term
securities for the same reason.
50
Limits on segmentation
• It rejects “pure expectations theory” assumption that
all bonds are perfect substitutes for each other.
• It cannot explain why interest rate rise on the bonds
of one maturity affects bonds of another maturity.
• Nor can it explain why yield curves slope upwards
when short term interest rates are low or are
inverted when short term interest rates are high.
• It would also seem less likely to hold true in
deregulated financial markets.
51
Liquidity premium theory
• It considers that risk averse investors will prefer
short term securities to longer term securities.
• As a longer investment exposes the investor to:
more risk (particularly price risk),
more compensation
 and hence higher rates on longer term investments are
expected.
• The level of compensation required may change
over time.
52
Liquidity premium theory (cont.)
• Advantages:
– Liquidity premium theory can easily be linked to
both the pure expectations theory and the market
segmentation theory.
– Help explain the shape of the yield curve for
majority periods of time (i.e. it can explain the
upward sloping or ‘normal’ yield curve).
• Disadvantages:
– only explains upward sloping curves;
– ignores risk preferences of suppliers of bonds.
53
Review of learning objectives
• Understand utility, risk and uncertainty
• Understand what determines interest rates
• Explain and construct the term structure of
interest rates
• Define and contrast the term structure of
interest rate related theories: unbiased/pure
expectations; market segmentation; liquidity
premium.
Case category
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270M CIS 3207 Programs CSCI 2132 CS270 CSE-381 COMP3230A CIS 212 CSI 333 FINM 326 FINM-36702 Introduction to Software Analysis EEE102 GNG1106 ECS 60 CS 161 CSCI851 CSE1222 EDPS0249 TCHR5003 ANTA02 BBUS1SBY SOSC 1140 MDIA2091 FINS3641 INSY 661 ITEC3040 CPSC 481 computer DEE3519 COMP304 CSE536 Microtheory OFFICE 280 CIVE50003 COSC2673 ECS784U CMPSC/MATH 455 AMA 505 CSE 158 BUS1040 FIT3179 FIT5202 Math 104A Math 111A MBUS107 COMPSCI 761 COMP3710 COMPSCI 316 COMP559 COMP557 CP1 1902 COMP 310 ECED 3403 COMPX523 AGCM 3103 EMET 7001 ENGR3821 CISC 124 IPC comp20005 CS 323 CS105 STAT 326 MATH4007 CS4551 COMP1000 ACIT 4640 ENVX3002 CS2034 FC712 algorithms CSCI 4155 CSI4142 POL 850 MATH20811 2B03 CSCI803 Economies COMP 2016 Architect TRADE INFO1110 FIT1043 networks Robotics ICS 31 ECEC-301 FIT2099 CS 3640 CSE1010 Computational COMP1001 CSE 231 CS10 FIT5166 CSE 400 CSCI561 Math 350 CO-496 ENGG6400 CSCI 1133 COMP3055 MATH 819 CSE 6363 CIS 555 CS4420 COMP0037 ECS 140A Spanning Tree Protocol network 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EBU5376 STAT6118 ECON 20110 COMU7000 average acceleration BUSI4412 BFF3121 BIT233 ECMM462 ETC3430 DESN2348 INTE2584 ENME502 MA3XJ INTE2627 MA2815 MA3AM L0101 Math 3MB3 CPCCBC4004 EEEM061 0502E220 APPLIED 6SSMN310 ENV 3310 PM2PCOL3 CONS6201 MATH502 FIT5003 EEEN313 MATH3001 MECH3460 ECON30009 COSC1252 Assembler COMP 3023 ENGG7601 COMP20005 COMP SCI 1103 ICSI 402 INF2C CS320 COMPSCI7064 ECE 3220 PROGRAMMAMING MIPS Computer Science 2413 AM3611 MSOA TE2101 FFT CMPSC-121 CSE 109 COMP SCI 7064 HCI CMP-5013A CCN2042 COMP3400 EEEN30052 CO4215 EE101 KIT107 CSE 421 CSE521 MCD4720 EECS 280 MIT 403 GRPC VG101 APiE EECE 1080C FIT3143 CSE 325 ISOM 3029 CS3307 State SIT255 Engineering MQF Modelling ACX3150 SIA322 ACCT90004 COMU7201 MGMT90018 WRIT1000 COMP3702 BISM1201 COMP7505 IDEA9106 CSE3SMT BFC5926 BFC5280 BFC5935 QBUS3330 ECON3700 IFN521 ECON2121 COSC2626 MA413 DDES9903 ENGG1300 COMP9337 CO2201 ACCT2002 ICM289 MMM054 MSBA-204 DIGM707 CSC2250 Econ312 EVAT python CAN404 LUBS2840 CSCI-GA.2250 COMSM0093 COMP281 AFM 333 IBUS1001 CP2501 Math 105A VE320 TEC101 SOCY2166 COM240 EFIM20033 ENGI4467 EFIM20034 EC 979 BE432 7EJ502 CSSE6400 COMP90025 Econ 312 ENG2031 ECO0006 EXERSCI 207 CAN209 ECO 137W FT312 ECO 2199 MATH32052 BDW4213 APS 360 SAS 6 CHME0017 PO92Q Economics 01AV MATH39512 MATH 5486 COMP8620 ISE102 ECON235 ECON 206 FI 345 PHAY0020 MATH0099 MATH0085 EFB106 PHY 134 MAE115 circuits Chemistry CSE12 MATH-UA 233 PHAS0038 COMP2140 CONMGNT 7049 COMP151101 ECON 485 ACX5903 ENGN6536 ARCH1162 Law PHAS0042 CCF1C03 MATH 351 Phys 139 AG942 MGT001371 APH106 ECON1051 MA4AM MA3Z7 NUMBER THEORY REST0006 SESS0026 STAT0023 TABL 2741 CMP4008Y EFIM10015 Acct 560 PSYC735 GEOG 5 ACCT3104 CSEC5616 PHIL1012 ITLS6111 ECON8022 5CCM226A compX123 MA4XJ R001 EWB LLP120 COMP643 ENG 103 ECON 23950 ACCT 207 FINC 616 Bio99 Math 137A Psychology BCPM0054 MATH20212 EC3450 CENV6141 PSY 205 CE335 CS365 Calculus ACSD INFT6800 MCIT INFO6030 PHYS 111LV H63EEJ ECON2151 ENGI 2181 MTRX1701 PLIT08009 CS240 Math 270 CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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