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Financial Engineering is very interesting.

- The theme is risk management -

Cat: ECO
Pub: 2000

Yukio Noguchi (野口悠紀雄)


Financial Engineering is very interesting


  1. Introduction
  2. Can be rich by financial engineering?:
  3. The theme of financial engineering is risk:
  4. Principles of distributed investments:
  5. Beta investment theory:
  6. Future contract:
  7. Option:
  8. Social technology opening up the future:
  1. 序文:
  2. 金融工学で金持ちになれるか:
  3. 金融工学のテーマはリスク:
  4. 分散投資の原理:
  5. ベータ投資理論:
  6. 先物取引:
  7. オプション:
  8. 未来を拓く社会的技術:
; Backwardation; Call/Put option; Capital market line; CAPM; CME; Contango; Covariance; Diversified investment; Efficient market; Exercise price; Expiration date; Financial futures; Forward contract; Index fund; Indifference curve; Interest parity theory; In (/out of) the money;Long/Short position; Marginal utility; Outright transaction; Pay-off; Portfolio separation theorem; Probability distribution; Risk premium; Sharp ratio; Stock option; Swap transaction; Tobin theorem; ;

>Top 0. Introduction:

0. 序:

>Top 1. Can be rich by financial engineering?

  • To understand financial engineering, the knowledge of economics, financial theory, financial practices, as well as mathematics and statistics are necessary.
  • One of the result of financial engineering is that there is no way of earning surely using the knowledge of this.
    • chart, or chartist who is a specialist to analyze or read chart of stock value.
  • >Top Efficient Market Hypothesis (EMH): (by Eugene Fame)
    • 'Weak': prices on traded of assets already reflect all past publicly available information.
    • 'Semi-strong': prices instantly change to reflect new public information
    • 'Strong': prices instantly reflect even hidden insider information.
  • Event study:
    • a statistical method to assess the impact of an event on the value of a firm.
    • time shift from the publication of an information until the impact of stock value.
    • counterevidence: Black Monday in Oct. 1987; about 20% drop of stock price without special event.
      • insider information; anomaly; bubble
  • >Top Index fund: mutual fund or exchange traded fund (ETF); can track a specified basket of investment like S&P500 or Dow Jones Industrial Average.
    • a stock name of 'Dow'; passive portfolio management
    • The market becomes efficient as long as there are people who don't believe the market is efficient.
    • Financial engineering contributes to avoid wasteful loss in investment; not to be imposed.
    • Modern science proved impossible to make time machine, perpetual motion machine, or alchemy.

1. 金融工学で金持ちになれるか:

  • efficient market: 効率市場
  • index fund: 投資信託; ダウ
  • event study: 当該企業の業績情報
  • 効率市場
    • 市場は情報に対して効率的か
    • Weak; Semi-strong; Strong
  • イベントスタディ:
    • 情報発表と株価の時間推移
    • →市場は概して効率的
  • インデックス・ファンド
    • Passive portfolio management; 市場全体の縮図に近いPortfolioを長期に運用
    • ダウという株
    • 誰もが信じれば非効率になる。
    • 市場が効率的なのは、効率的でないと信ずる人々がいるから
    • 本物の金貨が道に落ちている場合
    • 金融工学の方法論=無駄な損失の回避=騙されないためにも


>Top 2. The theme of financial engineering is risk:

  • Risk: potential of gaining or losing something of value caused by uncertain action.
    • our life if full of various risks; such as disease, accident, or disaster
    • agriculture by weather, fishery, hunting, and mineral exploration.
    • MTS (make-to-stock) to BTO (built-to-order)
    • from hunting to stock-farming; from fishery to aqua farming cultivation
  • >Top Risk Management:
    • Minimax principle
    • Risk: uncertainty having probability distribution
    • True uncertainty having no probability distribution
  • Expected value, variance and standard deviation (SD) (or volatility in finance):
    • law of large numbers; normal distribution
  • >Top Risk premium:
    • minimum amount by which the expected return on a risky asset must exceed the known return on a risk-free asset.
    • compensation for investor who tolerate the extra risk, compared to that of a risk-free asset.
      • hedger:
      • speculator:
      • to maximise the expected utility; convex curve to the top
    • >Top the marginal utility is digressive (law of diminishing marginal utility):
      • the first unit of consumption of a good or service yields more utility than the second and subsequent units.
    • Variance ($\sigma^2$): measures how far a data set is spread out.
      • Variance ($\sigma^2$): $u(X)=(X-\mu)^2$, where $\mu$ is mean.
      • Standard Deviation (SD) ($\sigma$)
    • St. Petersburg Paradox: (proposed by Nicolaus Bernoulli)
      • a particular lottery game that leads to a random variable with infinite expected value, but nevertheless seems to be worth only a very small amount to the participants.
        • People want to maximize 'expected utility' rather than 'expected profit.'
    • >Top 'Indifference curve': and equal utility curve
      • showing combination of two goods that gives equal satisfaction and utility. Each point on the curve indicates that the consumer is indifferent between the two.
    • Risk management: (>Fig.)
      1. Diversified investments
      2. Insurance contract
      3. Sales of risky assets, or forward contract
    • Decrease of SD by combination of investment: (>Fig.)
      • the risk of combination is smaller than the weighted average.
      • To minimize risk (or SD) is not the object of asset, but to maximize the return of investment. (Portfolio)
    • Investment Opportunities Curve: (>Fig.)
    • Efficient frontier:
      • An investment portfolio which occupies the efficient parts of the risk-return spectrum.; formulated by Harry Markowits in 1952.
  • Tobin's Separation Theorem:
    • Fund operation is available by adding no-risk asset (like government bond, cash, etc.) to the best risk-return portfolio, depending on each investor's risk allowance.
      • If the risk allowance is low, the investor prefers to have more non-risk asset or risk allowance is high, the investor prefers not to have no-risk assets, or raise return ration by leverage.
    • Fig:
    • separationthorem
      • Capital Market Line (CML); gradient of the line is risk premium.
    • >Top Modern portfolio theory:
      Harry Markowitz theory had not been attention by economists. But James Tobin extended his theory, establishing the separation theorem and market value of risk.
      • B point of the above figure is called safe asset, like government bond.
      • A certain point as a mix of safety asset and risk asset is shown by the blue line (risk premium, or market risk premium).
      • The indifference curve, an equally acceptable risk curve, which is chosen by a consumer, is shown here as green curve.
      • To gain the optimized combination, this line should contact the outmost point (D) of the investment opportunities curve (red curve).
      • This D point is determined irrelevantly by investors' preferences, i.e., mix of risk assets is determined independently from risk-return preferences of investors.(Tobin theorem, or Portfolio separation theorem)
      • Thus, the optimized portfolio for any investor is plotted on the above blue line (Capital Market Line).
      • The gradient of the blue line shows: (Risk asset return - safe asset return)/(SD of asset return); here the numerator shows risk premium of risk asset.

2. 金融工学のテーマはリスク:

  • risk: uncertain: likely turn out well or badly
  • expected value: 期待値
  • probability distribution: 確率分布
  • marginal utility: 限界効用
  • indifference curve: 無差別曲線
  • investment opportunities curve: 投資機会曲線
  • capital market line: 資本市場線
  • リスク: 確率分布のある不確実性
  • 期待値・分散・標準偏差
    • 大数の法則・正規分布
  • リスクプレミアム (期待収益率):
  • 限界効用逓減の法則
  • St. Peterburgの逆理
    • 人々が最大化するのは期待効用であって期待利得ではない。
  • 無差別曲線:
    期待効用が一定となる期待値と分散; 同じ効用が得られる財の組合わせ
    • 無差別曲線と等効用線
  • indifferencecurve
  • Market risk & unique risk:
  • uniquerisk
  • investopportunitycurve
  • モダンポートフォリオ理論:
    • 低リスク銘柄と高リスク銘柄による組合せパターン
    • 各人のリスク許容度に応じて株式と国債の割合を決める (効率的ポートフォリオ)
      • Index fund vs. Active fund
  • トービンのPortfolio分離定理:
    • 資本市場線 (CML)

>Top 4. Beta investment theory:

  • Each asset should be evaluated in relation to the optimized portfolio.
    • Return ratio of a certain asset is in proportion to the covariance of return of the asset and return of market portfolio:
    • $r-r_f=\beta(r_m-r_f)$
      where, $r$: expected return of a certain bond; $r_m$: expected return in the market; $r_f$: risk free rate, and $\beta$: beta coefficient.
      • 1776: Adam Smith, The Wealth of Nations: "The division of labour is limited by the extent of the market. "
      • If $\beta =1$: Return ration of a certain asset is same as return of market portfolio (Eg. Steel or electronics industry).
      • If $\beta >1$: has more volatility (high risk high return industry like venture business) , or,
      • if $\beta <1$: has less volatility (low risk low return industry, like electricity or gas utility industry).
  • >Top CAPM (Capital Asset Pricing Model): by W. Sharpe
    • $R_i-R_f=\beta_i(R_m-R_f)$
    • where, $R_i$: expected return on capital asset; $R_f$: risk-free rate of interest; $\beta_i$: sensitivity of expected excess asset returns to expected excess market returns; $R_m$: expected return of the market.
    • where, $R_m-R_f$: market premium; $R_i-R_f$: risk premium.

4. β投資理論:

  • security market line: 証券市場線
  • 証券市場線 (SML):
  • securitymarketline

>Top 5. Future contract:

  • Main purpose: to mitigate risk of default by either party in the period, requiring to put up initial cash, or margin (5-15% of the contract value).
    • 17C: Dutch future markets appeared. ; 1636 Dutch Tulopmania.
    • 1697: Dojima Rice Exchange established in Osaka, the first future exchange market.
    • 1864: Chicago Board of Trade (CBOT) standardized future contracts based on grain trading.
    • 1875: cotton futures were traded in Bombay.
    • >Top 1972: In Chicago Mercantile Exchange (CME), International Monetary Market (IMM) was established.; £, Mark, ¥ was listed.
    • 1975: GNMA, TB, CD, CP was additionally listed. (Financial futures)
  • >Top Forward contract vs. Future contract:
    • a non-standardized contract between two parties to sell or buy at the specified future time at a price agreed today.
    • Future contract: a standardized forward contract; a legal agreement to buy or sell something at a predetermined price at a specified time in the future (delivery time); contracts are negotiated at future exchanges.
    • Short position: sale of an asset that the seller does not won, anticipating the value will fall over time.
    • Long position: purchase of an asset anticipating the value will rise over time.
  • >Top Swap transaction:
    • A swap is a derivative contract where two parties exchange financial instruments.
    • Interest rate swap: between fixed interest rate and floating interest rate.
    • Foreign exchange (FX) swap: consumer and bank convert a currency into another as per agreed exchange rate.
      • Interest parity theory:
        (1+domestic rate)=(1+foreign rate)☓(1+foreign fluctuation)
      • Eg. ¥ rate=1%, USdol rate=10%, then $1.01=x・1.1$, thus $x=0.918$; USdol must be depreciated about 8.2%.
      • Outright transaction: two parties agree to buy or sell a given amount of currency at a predetermined rate at some point in the future independently; apart from counter forward transaction of hedge transaction.
  • Hedge transaction:
    • a type of derivative; to minimize loss by balancing transactions.
  • Margin:
    • to minimize credit risk to the exchage, traders must post a margin or performance bond, typically 5-15% of the contract value.

5. 先物取引:

  • future transaction: 先物取引
  • forward transaction: 先渡取引
  • Chicago Mercantile Exchange: シカゴ商品取引所
  • margin: 証拠金
  • expiration (or expiry) date: 約定日、決済日
  • Yield curve (利回り曲線): generally longer period is higher interest rate.
  • yieldcurve

>Top 6. Option:

  • Option:
    • to prevent the worst sitution, and gain profit even in unpreferable situation; withi paying some option money as the cost.
    • a contract which gives the buyer the right, but not obligation, to buy or sell an underlying asset at a specified strike price on specified date.
      • Call option: to sell at a specific price.
      • Put option: to buy at a specific price. (>Fig.)
    • In ancient Greece; Thales of Miletus, who acquired the right to use olive presses the following spring. The olive harves was larger than expected.
    • 1973; Modern stock options: The Chicago Board Options Exchage was established.
  • Present value is the best forecast of future value.
  • >Top Pay-off:
    • the profit gained by executing the option.
    • In case of call option, the pay-off per stock would be ¥900 (2000-1100), if the stock price was ¥2000. (blue line of Fig.)
      • Anyone who anticipates the stock price will more than ¥1100 would buy this option.
      • But the pay-off would be zero, if the stock price was less than ¥1100.
    • In case of put option, the pay-off would be zero if the stock price was more than ¥1100, and which would be positive (=in the money), if the stock price was less than that.
    • The exercise price is ¥1100 in the the above case.
    • Expiration date: European or American stype option:
      • European: the option is executable on the specific expiration date of the option.
      • American: the option is executable at any point during the contract date.
  • >Top Casualty insurance or convertible bond is a kind of option:
    • Casualty insurance: is a put option of at a certain price in case of casualty.
    • Convertibble bond: is a call option which can convert to stock at a certain price.
    • Warrant bond: with pre-emptive right to new share. The bond remains when the right is executed.
    • Stock option: a call option on the common stock of a company as part fo the employee's remuneration package.
  • History of option:
    • Genesis of The Old Testament: Jacob agreed to work 7 years for Laban in return for marrying Rachel the daughter of Laban.
    • 6C BC: Thales of Miletus (c624-c546 BC): Thales purchased the option to use the olive presses at a relatively low rate. When the harvest proved to be bountiful, and the demand of the press became high. If the harvest had failed, his loss was limited to the initial deposit he paid.
    • 17C Tulip bubble in Netherland: the whole seller bought the option right of tulip bulb; if it became expensive, the buyer execute the option, otherwise he buys the bulb in the market.
    • 1791: NY Stock Exchange:
    • 1973: CBOE (Chicago Board Option Exchange): listed 16 stock call options. In 1977, put option transaction has started. In 1982, TB was listed.
    • 1984 in Japan: FX option transaction over the counter has started. In 1989 bond option transaction started.
    • Black-Scholes equation: mathematical model for derivative investment; which shows the the option has a unique price regardless of the risk of the security and its expected return. The key financial insight is that one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently eliminate risk.

6. オプション:

  • long position: 買い持ちポジション
  • short position: 売り持ちポジション
  • swap deal (transaction): スワップ取引
  • outright transaction: single spot/forward transaction
  • hedge: protect by balancing
  • forward exchange contract: 先物為替取引
  • cream skim; cherry pick, nibble here and there: いいとこ取り
  • >Top call option/put option: buy option/sell option
  • in the money (ITM)/out of the money (OTM)
  • volatility:
  • $\Delta, \gamma, \kappa, \Theta$
  • discount rate; negative spread; loss margin; backwardation: 逆鞘
  • regular spread; positive spread; contango: 順鞘
  • exercise price: 行使価格
  • stigma: 不名誉、汚名
  • 先物取引: 契約により将来を固定する。
  • 先物の歴史:
    • 17C: オランダの先物取引 (チューリップ)
    • 1697: 堂島で米の先物取引
    • 1848: シカゴ商品取引所 (トウモロコシ・小麦)
    • 1875: ボンベイ綿花の先物取引
  • 先物取引と先渡取引:
  • Call option & Put option:
  • call_putoption

>Top 7. Social technology opening up the future:

  • Social engineering ICT requires:
    1. New business model using ICT
    2. New guideline to improve basic economic system, including deregulation, reform of corporate structure, employment environment.
    3. New funding mechanism particularly for ICT industry. New industry is usually risky. In US stock exchanges have functioned to promote such new industry, but in Japan those are insufficient. The technology for risk management is essential, which is financial engineering.
  • New business model of real estate industry
    1. more focussed on 'income gain' than capital gain. Risk management for real estate is also important.
    2. Financial engineering for financial transaction, particularly to estimate risk properly, including foreign exchange and interest rate as well as derivative transactions.
    3. Traditional risk has appeared in quantitate change, such as the change of trading volume. But current risk appears as the change of foreign exchange. And change of financial situation appears as the change of interest rate; these could be hedged in future contracts.
  • Economic engineering:
    • Engineering in economics as applied natural science.
    • Practical study, such as function of business school.
    • Role of Japanese financial institutions in applying latest financial technologies.
    • Delay in education of financial engineering.
  • Why Europe has first opened modern society? Modern science as well as engineering contributed as the booster of such movement.
    • Development of risk management, including book-keeping, stock company, insurance, etc.
    • Age of Discovery in 16C was private profit businesses; supported by merchant of Genoa, or Fugger family of Germany.

7. 未来を拓く社会的技術:

  • ITが要求する社会的技術
    1. IT活用した新たなビジネスモデル
    2. 期間的な経済制度の変革
    3. IT産業への資金供給の仕組み

  • 不動産業の新ビジネスモデル
    1. 不動産の利用を軸とする活動
    2. 不動産投資に伴うリスク管理

  • 経済工学
    1. 自然科学の応用としての経済工学
    2. ビジネススクールの役割
    3. 日本の金融機関の役割

  • なぜヨーロッパが近代を拓いたか
    1. リスク管理の技術: 会計、株式会社、保険
    2. 大航海は民間収益事業; ジェノバ商人、ドイツのフッガー商会
  • Seven major assets: composed of cash, stock (Jp/Foreign), bond (Jp/US), real estate (US), and commodity (>Fig.)
    • Portfolio-Av.: invested evenly in these 7 assets.
  • The portfolio of Japanese Pension Fund is: Bond-J 67%, Stock-J 11%, Stock-F 9%, Bond-U 8%, and Cash 5%
    • Portfolio-JPF: invested same as JPF.
  • High risk assets: Commodity, RE-U, Stock-J, Stock-F
    • Portfolio-highR: composed of these high risk assets.
  • How these seven assets increased in 30 years:
    • 830 Stock-F, 610 Port-Av, 580 RE-U, 570 Bond-U, 520 Port-JPF, 460 Bond-J, 280 Commodity, 260 Cash, 230 Stock-J.
  • >Top Sharp Ratio= (Return of portfolio - Return of non-risk asset)/(SD of Return of portfolio)
  • Portfolio in 30 years:


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