For 100 securities, there are 4,950. 100 үнэт цаасны хувьд 4950 байна.
Furthermore, in order to solve for the portfolio that minimizes risk for each level of return, a mathematical technique called quadratic programming must be used.
(Furthermore, in order to solve forthe portfolio)1 (thatminimizesrisk for each level of return), (a mathematical techniquecalledquadratic programmingmust be used).
A discussion of this technique is beyond the scope of this chapter. Ийм аргачлалын талаар өгүүлэх нь уг бүлгийн зорилго биш юм.
However, it is possible to illustrate the general idea of the construction of efficient portfolios by referring again to the simple two-assetportfolio consisting of assets C and D.
(However, itis possible to illustratethe general idea)4(of the construction of efficient portfolios)3(by referringagain to the simple two-assetportfolio)2 (consisting of assets C and D)1.
EXHIBIT 2.4 Portfolio Expected Returns and Standard Deviations for Five
Mixes of Assets C and D
Asset C: E(Rc ) = 12%, SD(Rc ) = 30%
Asset D: E(Rd) = 18%, and SD(Rd) = 40%
Correlation between Asset C and D = cor(Rc,Rd) = −0.5
Багц
С активын хувь
D активын хувь
Е(Rp)
SD(Rp)
1
100%
0%
12.0%
30.0%
2
75
25
13.5%
19.5%
3
50
50
15.0%
18.0%
4
25
75
16.5%
27.0%
5
0
100
18.0%
40.0
эх сурвалж: Frank J.Fabozzi, Harry M.Markowitz Investment Management 2003
Financial English course -2012 Unit Six Behavioural finance: Investor behavior Зан үйлийн санхүү: Хөрөнгө оруулагчийн зан төлөв
Behavioral finance has also had some success in explaining how certain groups of investors behave, and in particular, what kinds of portfolios they choose to hold and how they trade over time.
(Behavioral financehas also hadsome success)5 (in explaining (howcertain groups of investorsbehave)1)4, and in particular, (whatkinds of portfoliostheychooseto hold)2 and (howtheytradeover time)3.
A large body of evidence suggests that investors diversify their portfolio holdings much less than is recommended by normative models of portfolio choice.
(A large body of evidencesuggests) 3 that (investorsdiversifytheir portfolio holdings much less)1 (than is recommended bynormative models of portfolio choice)2.
French and Poterba report that investors in the USA, Japan and the UK allocate 94%, 98%, and 82% of their overall equity investment, respectively, to domestic equities.
(French and Poterbareportthat (investors in the USA, Japan and the UKallocate94%, 98%, and 82% of their overall equity investment, respectively, to domestic equities)1)2.
Indeed, normative portfolio choice models that take human capital into account typically advise investors to short their national stock market, because of its high correlation with their human capital.
(Indeed, normative portfolio choice modelsthattakehuman capitalinto account)1 (typicallyadviseinvestorsto short their national stock market)3, (because of its high correlation with their human capital)2.
Their portfolios therefore appear undiversified relative to the predictions of standard models that ignore the investor’s degree of confidence in the probability distribution of a gamble.
(Their portfoliosthereforeappearundiversifiedrelative to the predictions of standard models) (thatignorethe investor’s degree of confidence in the probability distribution of a gamble).
In particular, they provide evidence that in 401(k) plans, many people seem to use strategies as simple as allocating 1/n of their savings to each of the n available investment options, whatever those options are.
In particular, (theyprovideevidencethat in 401(k) plans)4, (many peopleseem to usestrategies as simple as)3 (allocating1/n of their savingsto each of the n available investment options)2, (whatever those options are)1.
The most prominent behavioral explanation of such excessive trading is overconfidence: people believe that they have information strong enough to justify a trade,whereas in fact the information is too weak to warrant any action.
(The most prominent behavioralexplanationofsuch excessive tradingis overconfidence)1: (peoplebelieve)3that (theyhave information strong enough to justifya trade)2,(whereas in fact the informationis too weakto warrantany action).
Building on evidence that men are more overconfident than women,Barber and Odean predict andconfirm that men trade more and earn lower returns on average.
(Building on evidence) that ( menare more overconfidentthan women,) (Barber and Odeanpredict andconfirm) that (mentrade more and earnlower returns on average).
Several studies find that investors are reluctant to sell assets trading at a loss relative to the price at which they were purchased, a phenomenon labelled the “disposition effect” by Shefrin and Statman.
Several studiesfindthatinvestorsare reluctant to sellassets tradingat a loss relative to the price at which they were purchased, a phenomenon labelled the “disposition effect” by Shefrin and Statman.
Odean finds that the individual investors in his sample are more likely to sell stocks which have gone up in value relative to their purchase price, rather than stocks which have gone down.
Odeanfindsthatthe individual investors in his sample are more likely to sellstocks which have gone up in value relative totheir purchase price, rather than stocks which have gone down.
Financial English Course Unit Five Derivatives Дериватив, үүсмэл үнэт цаас
Speaking Black-Scholes Call Option Valuation example
Suppose you want to value a call option under the following circumstances:
Stock price So = 100
Exercise price X = 95
Interest rate r = 0.10
Dividend yield
δ = 0
Time to expiration T = 0.25 (one-quarter year)
Standard deviation
σ = 0.50 First calculate
Next find N(d1) and N(d2). The normal distribution function is tabulated and may be found
in many statistics textbooks. The normal distribution function N(d), is also provided in any spreadsheet program. In Microsoft Excel, for example, the function name is NORMSDIST. Using either Excel or Table 15.2
(using interpolation for 0.43), we find that
N(0.43) = 0.6664
N(0.18) = 0.5714
Finally, remember that with
δ = 0,
Thus, the value of the call option is
C = 100 X 0.6664 - 95 e-0.10 x 0.25 x 0.5714 = 66.64 - 52.94 = $13.70
Source: Bodie, Kane, Marcus Investments 2007
Translation
Speculation and Hedging in the Currency Futures Markets: Are They
Informative to the Spot Exchange Rates Валютын Фьючерсийн Зах Зээл дэх Аз Туршин дамлах(Спекулятив шинжтэй) ба Хеджинг: Тэдгээр нь Спот Ханшинд Нөлөөлдөг үү
We present an empirical analysis in this paper investigating the relation between speculation and hedging in the currency futures markets and changes in spot exchange rates. (Wepresentan empirical analysis in this paper)2 (investigatingthe relationbetween speculation and hedging in the currency futures markets and changes in spot exchange rates)1. Энэхүү судалгааны ажлаар, валютын фьючерсийн зах зээл дэх аз туршин дамлах ба хеджинг болон спот ханшийнөөрчлөлтийн хоорондын хамаарлыг судалж импирик шинжилгээ хийлээ.
We are particularly interested to know whether futures trading activities convey valuable information upon potential price movements in major currencies including the British pound, euro, Japanese yen, and Mexican peso. (Weare particularly interested)2 (to knowwhetherfutures trading activitiesconveyvaluable informationuponpotential price movements in major currencies including the British pound, euro, Japanese yen, and Mexican peso)1. conveyupon............ in................. - нөлөөлөх ....... -д Британийн фунт, евро, Японы иен болон Мексикийн песо гэх мэт голлох валютуудад үнийн болзошгүй өөрчлөлтөнд фьючерсийн арилжааны чухал мэдээлэл нөлөөлдөг эсэхийг тодруулах зорилго илүүтэй тавьсан.
To extract the information content of futures trading activities, we transform trader positions into several econometric measures. (To extractthe information content of futures trading activities)1, (wetransformtrader positionsinto several econometric measures)2. transformtrader positionsinto - арилжаалагчдийн позицийг(- фьючерсийн гэрээг энд хэлж байна)руу шилжүүлэх Фьючерсийн арилжаалагчдийн арилжааны мэдээллийн агуулгыг аграгж ирэх зорилгоор арилжаалагчдийн позицийг эконометрикийн хэд хэдэн хэмжээсрүү оруулсан.
Other than the routine usage of net positions by type of traders, we construct an investor sentiment index which presents a relative rank of the current net position within the context of the historical range and thus largely reflects investors’ belief on the degree of bullishness or bearishness of the markets. (Other than the routine usage of net positionsby type of traders)1, (weconstructan investor sentiment index)3 (whichpresentsa relative rank of the current net positionwithin the context of the historical range)2 and (thus largely reflectsinvestors’ beliefon the degree of bullishness or bearishness of the markets)4. Арилжаалагчдын хэлбэрээр нь цэвэр гэрээг тогтмол хэрэглэх байдлыг нь харьцуулах зорилгоор түүхэн далайцын хүрээнд өнөөгийн цэвэр гэрээний харьцангуй зэрэглэлийг илэрхийлдэг хөрөнгө оруулагчдын хандлагын индексийг байгуулсанаар, уг зах зээл дэх хөрөнгө оруулагчдийн хашир болон өөдрөг байдлын түвшинг мэдэр боломжтой.
Investment sentiments are further distinguished by indicators of extremely bullish sentiment and extremely bearish sentiment. (Investment sentiments are furtherdistinguishedby indicators of extremely bullish sentiment and extremely bearish sentiment)1.
In addition, we develop a dating algorithm which facilitates us to identify the peaks and troughs of traders’ net position. In addition, (wedevelopa dating algorithm)3 (whichfacilitates)2 (usto identify the peaks and troughs of traders’ net position)1. Түүнчлэн, арилжаалагчдын цэвэр гэрээний өгсөх болон буурах үеийг тогтоох болзолт алгоритмийг бид боловсруулсан.
By design, these identified peaks and troughs represent the de facto extreme positions held by speculators or hedgers. By design, (these identified peaks and troughsrepresent)(the de facto extreme positionsheldby speculators or hedgers)1. Ингэснээр, эдгээр өгсөх болон буурах мөчлөг нь дамлагчид ба хеджерүүдийн бодитой эзэмшиж буй гэрээг илэрхийлдэг.
We show that peaks of speculative positions and troughs of hedging positions are highly predictive of future price continuations while troughs of speculative positions and peaks of hedging positions are generally negatively associated with future spot rate changes over short horizons. (Weshow)3 (thatpeaks of speculative positions and troughs of hedging positionsare highly predictive of future price continuations)2 (whiletroughs of speculative positions and peaks of hedging positionsare generally negativelyassociated withfuture spot rate changesover short horizons)1. Хеджинг хийсэн гэрээний өсөх ба буурах мөчлөг нь богино хугацаанд спот ирээдүйн ханштай ерөнхийдөө сөрөг хамааралтай байхад спекуляци хийсэн гэрээний өсөх мөчлөг ба хеджинг хийсэн гэрээний буурах мөчлөг нь ирээдүйн тогтмол үнийг таамаглах чадвар өндөр байна.
Our results, nevertheless, do not offer persuasive evidence that traders’ net positions per se and investor sentiments are systematically informative to potential price movements of foreign currencies examined except for the euro. (Our results, nevertheless, do not offerpersuasive evidence)3 that (traders’ net positions per se and investor sentiments are systematically informative to potential price movements of foreign currencies)2(examined except for the euro)1. per se- 1 хеджер ба аз туршин дамлагч бүрт ноогдох Еврогоос бусад тохиолдолд нэг хеджер ба аз туршин дамлагчид ноогдох арилжаалагчдийн цэвэр гэрээ ба хөрөнгө оруулагчдийн хандлага нь гадаад валютын үнийн болзошгүй өөрчлөлтөнд тогтолцоотойгоор нөлөөлдөг гэсэн бидний итгүүлэх үндэслэлийг бидний судалгааны үр дүн нотлохгүй байна.
For the latter case, we find that an increase of 10,000 euro contracts in speculators’ net long positions forecasts a rise in spot euro rate by about 0.04 percent, 0.16 percent, and 0.45 percent over subsequent 1 week, 4 weeks, and 12 weeks, respectively, while the same increase in hedgers’ net long positions predicts a drop in subsequent euro changes with comparable magnitudes. (For the latter case, wefind)3 that (an increaseof 10,000 euro contracts in speculators’ net long positions)1forecastsa rise in spot euro rateby about 0.04 percent, 0.16 percent, and 0.45 percent over subsequent 1 week, 4 weeks, and 12 weeks)2, respectively, (while the same increasein hedgers’ net long positionspredictsa drop in subsequent euro changeswith comparable magnitudes). Еврогын жишээний хувьд, спекуляторуудын цэвэр гэрээг 10000 еврогоор нэмэгдүүлэхэд еврогын спот ханшийг 1 долоо хоногт 0,04%, 4 долоо хоногт 0,16%, 12 долоо хоногт 0,45% орчим нэмэгдэх хүлээлттэй байхад хеджерийн худалдан авах цэвэр гэрээг мөн хэмжээгээр нэмэгдүүлэхэд еврогын ханшийг бууруулах хүлээлттэй байна.
Similar results emerge when sentiment index is used as predictor. (Similar resultsemerge)2(whensentiment indexis usedaspredictor)1.
We also document a strong contemporaneous connection between trader positions and spot exchange rate evolvements. (We also document a strong contemporaneous connectionbetween trader positions and spot exchange rate evolvements)1. Арилжаалагчдийн гэрээ ба спот ханшийн өөрчлөлтийн хоорондын байнгын хамаарал байгааг бид олж тогтоосон.
Our findings may have important implications for market practitioners, policymakers, and academics. (Our findingsmay haveimportant implicationsfor market practitioners, policymakers, and academics). Бидний судалгааны үр дүн нь зах зээлд ажиллаж буй мэргэжилтнүүд, бодлого боловсруулагчид болон судлаачдад үлэмж ач холбогдолтой юм.
It is particularly interesting, for example, to know whether the documented significant predictive power of the peaks/troughs of net position could be translated to profitability of trading strategies utilizing this sort of information. (Itis particularly interesting, for example)4, (to knowwhether)3 (the documented significant predictive power of the peaks/troughs of net position could be translatedto profitability of trading strategies)2 (utilizingthis sort of information)1. Иймэрхүү мэдээллийг ашиглаад, арилжааны ашигт ажиллагааны стратеги боловсруулах зорилгоор цэвэр гэрээний өсх ба буурах мөчлөгийг баримттайгаар таамаглаж болох эсэхийг тодорхойлох нь нилээд сонирхолтой юм.
Monetary authorities may also closely watch the trader position data to keep track of future exchange rate dynamics, and in turn insulate their effects on inflation and on economic growth. (Monetary authoritiesmay also closely watchthe trader position data)2 (to keep track of future exchange rate dynamics)1, and (in turn insulatetheir effectson inflation and on economic growth)3. Мөнгөний бодлого боловсруулагчдаас ирээдүйн ханшийн цаг хугацааны цувааг бүртгэх арилжаалагчдын гэрээний өгөгдлийг сайтар ажиглах нь эргээд инфляци ба эдийн засгийн өсөлтөнд үзүүлэх нөлөөллийг нь бууруулж чадна.
The results show that, regardless of statistical significance, speculative position measures are typically straight signals of future price movements while hedging position measures are generally contrarian indicators of potential spot rate changes. (The resultsshow)4 that, (regardless of statistical significance)1, (speculative positionmeasures are typically straight signals of future price movements)2 (whilehedging positionmeasures are generally contrarian indicators of potential spot rate changes)3. Статистикийн ач холбогдлыг нь үл харгалзвал, спекуляци шинжтэй гэрээ нь ирээдүйн үнийн өөрчлөлтийн шулуун дохиог хэмждэг байхад хеджингийн гэрээ нь эсрэгээрээ спот ханшийн болзошгүй өөрчлөлтийн үзүүлэлт байдаг болохыг бидний судалгааны үр дүн харуулсан.
Researchers may be interested in this finding as it lends support to competing theories such as hedging pressure or positive feedback trading. (Researchersmay be interested inthis finding)2 (asitlendssupport to competing theoriessuch as hedging pressure or positive feedback trading)1.
