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FINS5513 Financial Instruments
Creation date：2024-05-16 17:50:08
Belonging category：金融Finance
Financial Instruments

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FINS5513 Lecture 1A

Financial Instruments
and Securities Trading
❑ 1.1 Financial Instruments
➢ Overview
➢ Debt Securities
• Money market
• Bonds and bond indices
➢ Equity Securities
• Equity indices (price weighted vs value weighted)
➢ Derivatives
❑ 1.2 Securities Trading
➢ Issuing Securities
➢ Costs of Trading
• Order types
• Spreads and commissions
Lecture Outline
2
1.1 Financial Instruments
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Introduction
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Overview of Asset Classes
Financial Assets
A non-physical, liquid asset that
derives its value from a claim
on future cash flows
Debt Securities
Promises a fixed stream of
income or a stream of income
determined by a specified
formula
Equity Securities
Represents an ownership
share in a corporation
Derivatives
Provide payoffs that are
determined by the prices of
other assets
5
Overview of Asset Classes
Financial
Assets
Debt Securities
Equity Securities
Derivatives
Money Markets
Bond Markets
Preferred Stock
Common Stock
Futures
Options
6
Debt Securities
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Short term debts (maturity of less than 1 year), highly marketable and liquid:
❑ Treasury bills – T-Bills (Government issued)
❑ Certificates of Deposit - CDs (Bank issued)
❑ Commercial Paper - CP (Company issued)
❑ Bankers Acceptances
❑ Eurodollars: dollar-denominated deposits in banks outside the U.S.
❑ Repos and reverse repos: Short-term loan (typically overnight) backed by government
securities
❑ Fed Funds: Overnight loans between banks for Fed deposits
❑ Brokers’ Calls – rate brokers borrow from banks
❑ LIBOR Market – interbank lending. Reference rate for many loans
Money Market Instruments
8
❑ LIBOR (London Inter-Bank Offer Rate) has historically been an important reference rate for a
wide variety of transactions, both in the interbank market and the corporate loan market
➢ Based on a survey of rates reported by participating banks rather than actual transactions
➢ Interbank lending has become more sparse recently, resulting in less reference points
➢ As the sample size is decreasing and following a scandal arising from manipulation of the
rate in 2012, the search for a replacement is on
❑ LIBOR proposed to be phased out by 2021 and replaced by averages using actual
transactions
➢ SONIA: Sterling overnight interbank average rate (GBP)
➢ SOFR: Secured overnight funding rate (USD)
➢ TONA/ TONAR: Tokyo overnight average rate (JPY)
➢ ESTER / €STR: Euro short term rate (EUR)
➢ AONIA: RBA interbank overnight cash rate (“cash rate”) (AUD)
Money Market Instruments
Further Reading 1AR1: “Understanding the LIBOR Scandal”
9
Medium to long term debts (1 - 30+ years)
❑ US Treasury Notes and Bonds (T-Notes and T-Bonds)
❑ Inflation-Protected Treasury Bonds (TIPS)
❑ Federal Agency Issues eg Federal Home Loan Bank (FHLB), Fannie Mae, Freddie Mac
❑ International Bonds
➢ Eurobonds – bond denominated in a currency different to the country where it’s issued
• E.g. Dollar bond issued in UK = Eurodollar bond
➢ Foreign bonds – same currency as the country of issue but issued by a foreign borrower
• E.g. Yankee bond = dollar bond, sold in US, by non-US issuers
❑ Municipal Bonds – tax advantaged
❑ Corporate Bonds
❑ Mortgage-Backed Securities
Bond Markets
10
❑ Major indices: Merrill Lynch, Barclays, Citigroup
❑ Challenges:
➢ Wider universe: While a company may have 1 or 2 types of stocks, a company may have
numerous bonds on issue (10+)
➢ Illiquid: A significant number of bonds are illiquid and infrequently traded
➢ Turnover: Bond indices turn over more than stock indices as the bonds mature (highly
dynamic)
Bond Indices
11
Equity Securities
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❑ Common stock
➢ Limited liability
➢ Residual claim
➢ Perpetuity – no fixed term
❑ Preferred stock: Fixed dividends
➢ Dividend is cumulative (and commonly fixed)
➢ Priority over common stock
➢ Often a perpetuity
❑ American Depository Receipts (ADRs)
➢ Certificates traded on US exchanges representing ownership of shares in foreign firms
➢ Created as a simplified way for foreign firms to satisfy US security registration requirements
➢ Most common way for US investors to trade shares in foreign corporations
Equity Securities
13
❑ Many stock market indices exist:
➢ Dow Jones Industrial Average (DJIA) – 30 large U.S. blue-chip stocks
➢ S&P500 – 500 largest U.S. stocks by market capitalisation
➢ NASDAQ Composite; NYSE Composite; Wilshire 5000
➢ ASX200 for Australia; FTSE for UK; Shanghai Index for China; Hang Seng for Hong Kong;
Nikkei for Japan
❑ How are stocks weighted?
➢ Price weighted (DJIA)
➢ Market-value weighted (S&P500, NASDAQ)
➢ Equally weighted (Value Line Index)
❑ Indices are not traded – however investors can buy into funds which track an index such as:
➢ Index mutual funds – see 1.4
➢ Exchange traded funds (ETFs) – see 1.4
Stock Market Indices
14
Price Weighted Index
❑ Price Weighted Index = average price of all stocks in the index
❑ In its simplest form, add up all the prices of stocks in the index and divide by the number of
stocks in the index:
ℎ = =
ℎ
ℎ
❑ The % change in a price weighted index is equal to the return on a portfolio that invests in
one share in each stock in the index
❑ Example 1A1: Calculate the change in a price weighted index of the following stocks:
➢ Step #1: Calculate PWI in Period 1 = (370 + 55 + 135 + 160) / 4 = 180.0
➢ Step #2: Calculate PWI in Period 2 = (350 + 45 + 140 + 165) / 4 = 175.0
➢ Change / return on a 4-stock portfolio = 175 / 180 - 1= -2.78% or (175 – 180) / 180 = -2.78%
Period GS KO APPL JNJ
Period 1 $370 $55 $135 $160
Period 2 $350 $45 $140 $165
15
❑ In the simplest case, the divisor (d) in the PWI is the number of stocks
❑ However, when stocks are replaced in the index or undertake a stock split, the divisor needs
to be amended. We do this as follows:
Revised divisor = =
ℎ ℎ ℎ
ℎ ℎ
❑ Example 1A2: Suppose Coca-Cola (KO) were replaced in the index by Microsoft (MSFT).
Keep all other prices equal. Calculate the PWI divisor:
➢ Step #1: Calculate PWI in Period 1 = (370 + 55 + 135 + 160) / 4 = 180.0
➢ Step #2: Calculate revised divisor (from above) d = (370 + 280 + 135 + 160) / 180.0 = 5.25
➢ Verify revised divisor 5.25 (from 4 previously) gives the same PWI as before the
replacement of KO with MSFT: (370 + 280 + 135 + 160) / 5.25 = 180.0
Price Weighted Index
Period GS KO MSFT APPL JNJ
Pre-change prices $370 $55 N/A $135 $160
Post-change prices $370 N/A $280 $135 $160
16
❑ A Value Weighted Index (VWI) is calculated based on market capitalisation of index stocks
❑ Each stock is weighted in the index proportional to its current market capitalisation
❑ Label the current period t and the previous period t-1. To calculate we need − 1 :
= − 1 ×
ℎ ℎ
ℎ ℎ −1
❑ Example 1A3: The index value of the S&P500 in the previous period (t-1) was 4000. Based
on the prices and market capitalisations below, calculate the S&P500 in the current period (t)
Value Weighted Index
Period GS KO APPL JNJ
# of Shares mn 340 4,300 16,700 2,630
Price MV $bn Price MV $bn Price MV $bn Price MV $bn
Period t-1 $370 125.8 $55 236.5 $135 2,254.5 $160 420.8
Period t $350 119.0 $45 193.5 $140 2,338.0 $165 433.95
17
➢ Use formula to calculate revised S&P500:
= 4000 ×
119.0 + 193.5 + 2,338 + 433.95 = 3084.45
125.8 + 236.5 + 2,254.5 + 420.8 = 3,037.6
➢ VWIt = 4,061.7 which is an increase of 4061.7 / 4000 -1 = +1.54%
❑ Price movements were the same as for the PWI, but the PWI index moves down -2.78%,
while the VWI moves up +1.54%
➢ This is because Apple moving up has a much greater impact on the VWI due to its market
cap being significantly greater than the other stocks
❑ The example demonstrates that in a VWI, larger companies account for much of the
movement; while for a PWI, smaller companies have more of an impact
❑ VWI do not have to be adjusted for events such as stock splits, dividends etc
❑ As fund managers focus on maximising the risk-adjusted value of their portfolios they are
significantly more likely to benchmark against a VWI (S&P500) than a PWI (DJIA)
PWI vs VWI
Video 1AV1: “Here’s how stocks get booted from the Dow” Excel 1AE1: “1A PWI vs VWI” 18
Derivatives
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❑ Derivatives are securities whose value is dependent on the value of other assets, such as
commodity prices, bond and stock prices, or market index values
❑ Forward – a deferred-delivery sale/purchase of an asset with the sales price agreed on today
❑ Futures – similar to a forward
➢ Carries an obligation to make or take delivery of an underlying asset at a price determined
today but settled at a future date
➢ Stipulates the quantity and specifications of the underlying asset
➢ Differences to a forward include:
• Standardised contract – more liquid and tradeable
• Trades on an exchange – mitigates counterparty risk (the exchange is the counterparty)
• Marked to market, with (daily) margin requirements – see 1.3
Futures and Forwards
20
Options
❑ A call (put) option gives the holder the right (but not the obligation) to buy (sell) an underlying
asset:
➢ At the exercise or strike price
➢ On or before the expiration date (depending on the type)
❑ Exercise the call option to buy the asset if market value > strike
❑ Exercise the put option to sell the asset if market value < strike
❑ The purchase price of the option is called the premium (both calls and puts)
➢ Buyer pays the premium / Seller (writer) receives the premium
❑ If the holder exercises the option, the option writer must make (call) or take (put) delivery of
the underlying asset
21
1.2 Securities Trading
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Issuing Securities
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❑ Public companies
➢ Issued stock is publicly listed on an exchange such as the NYSE, ASX
➢ Known as publicly traded, public companies, or listed companies
❑ Private companies
➢ Issued stock do not trade on an exchange – also known as unlisted companies
➢ Lower liquidity and less public disclosures
❑ Primary Market
➢ Market for newly-issued securities
➢ Proceeds raised from the issue flow directly to the company
➢ Firms issue new securities to the public (often through an underwriter)
❑ Secondary Market
➢ Investors trade previously issued securities among themselves
➢ Proceeds flow between investors that purchase/sell securities and not to the company
Security Issues
24
Primary vs Secondary Market
❑ The primary market (first time issue of securities) consists of:
➢ Initial Public Offerings (IPOs)
➢ Follow-on offerings (or a “seasoned equity offering”)
❑ Follow-on offerings refer to any issuance of new shares for companies already listed on an
exchange (i.e. any new share offering subsequent to an IPO)
➢ For example: rights issues, private placements of new shares etc
➢ Proceeds raised from the issue flow directly to the company
❑ The secondary market consists of:
➢ Trading amongst investors on exchanges
➢ Secondary market offerings
• Shares sold by existing shareholders (often called “block trades”)
• Non-dilutive to shareholders as the share count stays the same (they sell directly to each
other and the company receives none of the proceeds)
Further Reading 1AR2: “IPOs: Profiles are high: Returns?”
25
Costs of Trading
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❑ Market orders:
➢ No price indication – trade at the prevailing market price
➢ An instruction to trade a quantity at the best price currently available in the market
➢ Market order example: Buy 1000 shares in BHP at market
➢ Advantage: timely, executes immediately. Avoids price moving to a disadvantageous level
➢ Disadvantage: must pay the bid-ask spread. Price may move to a more advantageous level
❑ Limit orders:
➢ Price indication – trade at the best price available if it is no worse than the specified limit
price
➢ Limit order example: Buy 1000 shares in BHP at $46.50
➢ Advantage: may get a good price for the trade. Avoids paying the bid-ask spread
➢ Disadvantage: the trade may not execute (execution risk)
Order Types
27
❑ Explicit costs – direct costs of trading such as:
➢ Commission - fee paid to the broker for facilitating the transaction
• Calculated based on the total transaction size
• Range from 0% - 0.1% for online trading platforms to 1%+ for full-service brokers
➢ Transaction taxes, stamp duties, exchange fees etc
❑ Implicit costs – indirect costs such as:
➢ Bid-ask spread
• The difference between the bid and ask prices
➢ Market impact costs
• The effect of the trade on market prices
• Large buyers (sellers) must raise (lower) prices to encourage other investors to trade.
Minimal impact from small orders
• Delay costs (slippage) – suboptimal prices paid/received arising from delayed execution
of a trade due to its size or opportunity costs – profits not realised due to unfilled trades
Costs of Trading
Further Reading 1AR3:
“How no-fee stock trading is
changing the stock market”
28
❑ Bid-Ask spread – cost of trading with a counterparty directly (or through a broker/dealer):
➢ Bid: price at which the counterparty is willing to buy
➢ Ask: price at which the counterparty is willing to sell
➢ Bid-Ask spread: Ask - Bid
❑ Market orders – buy at the ask price / sell at the bid price
❑ Limit orders – place an order at a preferred bid (ask) price if you wish to buy (sell)
❑ Example 1A4: Using the transaction information below, calculate the trading costs (assume
the full cost of the spread) and net proceeds paid/received from a market offer trade
Spreads and Commissions
Buyer Seller
Bid-Ask $52.00 - $52.50 $32.70 - $33.00
# of Shares 0.5 million 2 million
Commission 0.20% 0.15%
29
➢ Market offer - the buyer buys at (“hits”) the ask and the seller sells at (“hits”) the bid
➢ For the buyer, commissions add to the cost of the trade. For the seller, commissions
reduce the proceeds from the trade
➢ Buyer Pays: 0.5m x 52.50 x (1 + 0.2%) = $26,302,500
Cost of trade: Spread = 52.50 – 52.00 = 50c
0.5m x 52.50 x 0.2% + 0.5m x 50c = $52,500 + $250,000 = $302,500
➢ Seller Receives: 2m x 32.70 x (1 – 0.15%) = $65,301,900
Cost of trade: Spread = 33.00 – 32.70 = 30c
2m x 32.70 x 0.15% + 2m x 30c = $98,100 + $600,000 = $698,100
Spreads and Commissions
Ask price
Bid price
30
❑ BKM Chapters 3 and 4
❑ 1.3 Trading on Margin: Long and Short
❑ 1.4 Asset Management Industry: Investment Companies, Hedge Funds and ETFs
Next Lecture
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CSCI262 SCC.311 COMP8101 IAB320 CHC5028 TSP ICC565 CS512 320SC COMP2396 COMP207 SVM BSCH EECS 2101 COMP3230 CEG3136 INFO 3440 EE3009 MGT7174 COMP 3334 ECON20120 Econ 702 CFRM 505 CS4001 CSE 328 AMATH 482 ENG2008 MATH39522 DTS101TC CSC318 EDUC 124 NBA 5110 ECON0125 ELEC7310 EEP101 ECE 777AE MDS 6112 Bioc0036 ACCFIN5246 STA 404 CFRM505 Chinese 2241G MATH 376 AUENV 218 ELEC0006 ACCT 3230 FIN3020 ENVM3115 CMPSC 464 EE 4233 CST 8284 ENGI 2211 EEB240 COMP52715 PHYS1120 ECON0019 MAT187 FINN1037 CSci 5421 7SSMM803 STAT 400 LUBS5996M ELC5216 STATS 4A03 ENGG1003 BADM 3661 DATA423 ST332 ECO2121 6406ELE IB3K20 CSE 465 CSE115 CMPUT 206 ecs150 INU1111 QM222 DTS204TC MATH2319 CPT108 SENG6110 MATH3041 INFS3604 MA 4704 CIVIL 750 EEEE4123 CS 3800 comp3511 MEC206 CSCI-UA.202 IOM 302 NBS8295 BMS 201 ECON 3018 ESE 605 ADM3225 STAT7038 Economics 409 ECON 503 MSE800 4SSMN902 IEOR E4106 FRE6831 ISE 563 MATH 451 ECON0001 COMPSCI369 CITS4402 MA1608 MQBS1030 MUSC1982 CITS4012 ACC202 BAFI1026 MA117 ECON5074 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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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4061 ECON 8820 INT104 ITE3713 CS551J ECM1410 CSMBD21 COMP 2012 CISC221 Code SCC312 COMP639 CMPSC 221 system COMP3217 COMP1721 ENG5056 Math 466 COMP0039 MFIN 5400F FINN40915 EENG31400 MODL5007M ​EEET 3050 EEET 3050 Quantitative Methods mathematics COMP1921 FIN3309 VE311 ESCI 1908 FIT5057 COSC2446 COMPUTING Math 110A EE 567 MATH10098 CISC642 EE10134 ECE 321 MTH2051 SIT 281 EEE3314 ELEC273 COMP5930M CE322 ELEC270 EE5101 MCEN90008 MTSC 887 Probability ENGN4528 MAE 424 MA2552 EBU5303 CHEM10600 EBU6018 ELEC2103 ELEE 5200 CSE 535 COMP6528 IS6153 IS3S664 BUSANA 7003 QTS0109 ECO3152B ENGR 227 LCSCI4208 MATH32051 ECS776P MGMT3004 N1551 JAVA ROB-6213 TNS3113 BEEM062 COMP47670 4SSMN903 BST 833 COEN 146 BASC0003 CAS EC501 Networks CSIT940 ELEC372 ACCFIN5034 Math 3527 DATA4000 INT102 FND109 MMM071 ROB6213 ETF5650 ECON 445 QMSS 301 Econ 320 PHY 4390 FIN 111 FINN41615 ECS 116 MTH6158 IOE 552 STA 141B Math 413 ECON3016 Physics 4303 Numerical BFF5270 EECS 111 FINANCE 251 COMP814 MGSC 410 ECON0051 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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