Research Articles Base: Financial Risk Management

ASSIGNMENT ON IMPROVING DEPARTMENTAL FINANCIAL MANAGEMENT

Introduction             This paper highlights a global firm, Pepsi, not to discuss how it outperformed Coca Cola in a recent Forbes press release () but more interestingly how it controls its budget.  However, this can have some implications to this century-old realized achievement.  The assignment will discuss the financial situation of Pepsi based on its 2003, 2004 and 2005 financial information (  2006 financial statements).  This will be followed by reviewing and evaluating how Pepsi improve its budget control in recent years and how it affects its financial performance.  Lastly, expectations on the future of the firm’s budgeting control are discussed.                     The Financial Situation of Pepsi             Based from the consolidated statement of income, net revenues increase in 2005 at billion marking a constant billion rise per year since 2003.  This means that the firm continues to achieve its objective for stable growth considering that its cost of sales for 2005 has increased by 0 million compared to previous years.  The revenue stability is also caused by the deferment of any restructuring and merger strategy for the current year.  By doing so, the company has concentrated its efforts to improve its business-level strategy and enhance customer value.  In addition, the global firm prevents excessive costs of change adjustment and implementation which would have both organizational and financial adversities.               There are four major subsidiaries for Pepsi; namely, Frito-Lay North America, PepsiCo Beverages North America, PepsiCo International and Quaker Foods North America.  Although it is known for its beverages division, its snack division Frito-Lay took the crown away from the beverages particularly in North America with billion more revenues for the past three years including 2005.  Divesting the pasta subsidiary of Quaker Foods in 2003 suggests how the firm strategically withdraws inefficient operations because Quaker revenue contribution consistently increases 0 million from 2003 to 2005.  The divestiture strategy on inefficient operations does not only provide the firm with positive net gain in the sale but also redeem its long-term growth efforts.  The operating profit of Frito-Lay is the highest among the divisions at 38% for 2005.  Accordingly, Quaker and PepsiCo North America suggest efficiency as their net revenues are non-proportional with their operating profits contributions; namely, 5% against 8% and 28% against 30% respectively.  Astonishingly, the highest net revenue contributor at 35%, PepsiCo International resulted to only 24% operating profit contribution.  This financial highlight shows how smaller subsidiaries outweighs net financial performance of bigger ones.                Based from its statement of cash flows, its operating activities provided .9 billion in cash compared to .1 billion in 2004 which is greatly affected by lower taxes paid.  This brings into the spotlight the importance of auditing functions to evaluate the wealth maximizing capability of financial statements.  However, the increase is held down by pension plan contributions that reached 3 million compared to last year’s 8 million.  This would suggest that the firm may test other human resource incentives for motivation probably at short-term stage.  General Motors is facing solvency difficulties because its diminishing profits cannot cover its pension plans forcing it to sell some of its major subsidiaries like its financial service arm.               Further, investing activities are largely dedicated for capital spending from 2003 and 2004 at around constant .3 billion.  The capital spending in 2005 has increased to 0 million which was basically funded by its sale of PBG stocks that reached 4 million.  This account is idle for the last two years which implied that such strategy is intended for aggressive investing activities.  In addition, the sale of property, plant and equipment also is increased for the current year which also submitted to the purpose of PBG sale.  To enforce Frito-Lay position, it also invested in snack ventures in Europe which is done only in 2005.  Portfolio investments is also active for the year at 5 million compared to 2004 ( million) and 2003 ( million).  This means that the firm is facing higher risk because it does not control these associates.  In effect, close coordination with its fund managers is needed to maximize its returns with minimal risk associated with such investment.  For the past three years, the firm is consistently investing in short-term investments at 0 million level.  This can be an ideal amount to support and rationalize the risk of capital spending which in nature are long-term investments.                     The financing structure of the firm shows how its proceeds from long-term debt issuances reduced in 2005 at million compared to 4 million.  There can be no hard conclusions for this as its can suggest that maturity dates are not yet due.  An important consideration, however, is if the firm can shorten its maturity dates in order for its cash flow maintain its upbeat standing.  In contrast to this, it has able to pay a mere 7 million for the current year in long-term debt compared to 2 and 641 in 2004 and 2003 respectively.  In effect, it has strategically situate itself in a position that it would not enjoy continuous cash inflow with its long-term receivable but also associated with minimal outflows in its opposite obligations.  On the other hand, cash dividends paid remained rising at a constant rate for the last three years while share repurchases for both common and preferred stocks remained in constant amounts.  This is an indication that the firm has substantial control in its financing strategies backed up by its ability to pay the short-term return requirements of its shareholders.               Based on the consolidated balance sheet, the current assets of the firm increase by .5 billion from 2004 to 2005 which balanced the increase in long-term assets.  If observed, the majority of accounts in the asset portion reflected a consistent increase which means that the firm is fairly stable and solvent.  On the other hand, its current obligations settled at billion while long-term debts are at .3 billion.  This position is very risky for the firm since it only has a .5 billion in current assets to cover its billion current liabilities.  However, the firm continuously receives positive credit rating from Moody’s and Standard and Poor’s which maintained their access to global financial markets.  In the equity side, issued common stocks for the year remained the same from 2004 with issuance worth million.  Retained earnings are surprisingly increased by billion despite of the increased dividend pay-out mentioned earlier.  In effect, the income-generation of the firm should not be undermined which could also suggest why it has able to receive positive credit ratings and borrow short-term debts despite minimal current assets.                Income per common share (basic) amounted to irregular swings from 2004 increase of .38 to 2005 decrease of .02.  Income per common share (diluted), on the other hand, resulted to the same direction with 2004 increase of .36 and 2005 decrease of .02.  Aside from the implication that the firm’s basic and diluted earnings per common share are similar, it had to make contingent strategies to minimize negative speculations about its income generating capability.  This results to increasing dividend per share from 2003 to 2005.  By doing so, the firm is in the position to be a business aggressive although the fact that 2005 return on invested capital reduced to 22.7% compared to past years of 27% level may adversely affect the risk-taking decisions of its shareholders.  The pressure of performing well in earnings, however, is mitigated by stable long-term debt at billion level for the past two years coupled by increasing total assets since 2003.  In effect, it is able to maintain share prices in manageable level and even reaching a 3-year record at the end of 2005 fourth quarter stock price closing at .   Financial Situation Summary   Financial Account Performance Net Revenue Positive Cost of Sales Moderately Negative Frito-Lay Positive PepsiCo North America Moderately Positive PepsiCo International Moderately Negative Quaker Moderately Positive Operating Activities Positive Tax Payments Positive Pension Payments Moderately Negative Capital Spending Moderately Positive Sale of Stocks Moderately Positive Sale of Property, Plant and Equipment Moderately Positive Portfolio Investments (Non-Control Associate) Moderately Negative Short-term Investments Positive Long-term Debt Proceeds Moderately Negative Long-term Debt Payments Positive Cash Dividends Positive Share Repurchases Positive Current Assets Positive Long-term Assets Moderately Positive Current Liabilities Negative Long-term Liabilities Negative Retained Earnings Positive Income Per Common Share (Basic/ Diluted) Moderately Negative Dividend Per Share Moderately Positive Return on Invested Capital Negative Long –term Debt Moderately Positive Total Assets Positive Share Price Positive       The Nature of Budget Control             In general, budget control is central to the key management areas of an organization; namely, planning, monitoring, controlling and evaluation.  Specifically, the quantitative approach to budgeting makes the process to create accountability on the part of decision-makers ( 2000).  On the contrary, other benchmarking/ targeting activities that merely result on qualitative characteristics of the goals do not only eradicate the opportunity for measuring the output but more importantly lessen the accountability attached to each decision-maker.    Budgeting and budget control preserves the objectives of the firm/ strategy, guides the execution of plans and makes results measurable for comparison/ analysis.  For example, the statement that “sales department aims to increase sales growth by 2% next month” connotes accountability than excluding the parameters 2% and next month.  Thus, budgeting should be prerequisite to budget control to be able to have something to control to.  Otherwise, the objective value of budget control will be worthless as managers would tend to insert their own subjective criteria.                          The fundamental purpose of budget control is to create and maintain accountable decision-makers/ implementers within the organization ( 2000).  Since it uses before-strategy-implementation inputs (probably historic data) to come-up with realistic and optimal strategy, actual strategy implementation is expected to adhere and lead to the intended goals.  Failure to comply would result to two-sided adverse effects against the organization; namely, low revenues and high expenses.  The budget for every department of the firm is bargained and ultimately given in order for the inputs skim down to outputs.  With such continuous occurrence, the firm might face bankruptcy.  The role of budget control is to prevent this from occurring by affecting budget preparation, rationalizing results of a financed strategy, monitoring periodic performance and evaluating the actual results with the pre-determined ones.              Pepsi’s Budget Control: Improvements through the Past Years             Software utilization.  In 2001, the firm’s Middle East and North American divisions had applied oracle e-business suite and technology products ( 2006). This resulted to improved financial controls since there were also improvement in the efficiency of sales reporting, tracking of sales promotions, inventory control and settlements.  The technology allows the firm to monitor and measure business needs as they emerge, thus, appropriation of the pre-determined budget tends to be more contingent not fixed.  Budget control should be emphasized in these regions especially in the Middle East to protect the firm’s rare market leadership against Coca Cola.  As a result, both its internal (manufacturing) and external customers (distributors) including suppliers are benefited from faster creation of financial data that aid in decision-making.  This is because the technology is complemented in shortening the firm’s monthly financial closing by up to 20 days.  As decision-making requires financial inputs to rationalize decision alternatives, the firm has provided an efficient working and contracting environment among its business partners.             Seeking consultancy services.  It is a smart and useful move for the firm to expose its organizational problems with an outsider.  By doing so, biases and lesser motivation to study and improve key business areas would be possible.  As the saying goes, “Mirrors are deceptive.”  As a result, the firm took the services of PA Consulting Group for a task to reduce its billion operating costs ( 2002).  The problem posted a budget-out-of-control problem to the firm that places them below industry’s best practice when it comes to budgeting.  Since the firm managers are operating in a volatile and demanding environment, the Group suggested a fast framework model in order to offset the inability of these managers to timely access relevant information essential to an effective decision-making.  The new business model was tried in the US and Canadian operations that resulted not only to productivity gains but also cost reductions by as much as 20% within weeks.  The program included productivity tracking, staff and resource scheduling and staff appraisal requirements.  The success of the Group’s advice had impressed the officials of the firm that will likely resort to the aid of the former in the future.               Dissolution of ineffective partnerships.  In 2002, the firm’s Sichuan factory in China was filed to be dissolved due to loose of control of Pepsi over the venture ( 2002).  The firm had accused the government-held partner of looting in favor of vacations and expensive cars which ultimately provided local managers with greater control.  Local managers were also indicted to bar Pepsi auditors to enter the factory and inspect account standings.  In effect, check-and-balance was not possible in the present structure which made budget control a difficult and lapse-sided condition for the firm.  Resources, even though not confirmed, are not allocated optimally from the mere absence of audit.  This had cause the firm to throw accusations just to give rationale behind the audit barring.  The financial and organizational including business strategies were diminished by the happening.  The socio-political background of local managers served as the bottleneck (that even referred Pepsi as practitioner of commercial hegemonism) that led the firm to drop one of its key factories in exploiting the large customer base available in the country.  The decision, however, emphasized the importance of budget control and budget monitoring in consolidating corporate/ global results in which the firm should integrate into one financial system.   Financial Situation after the Improvements Improvements Results Software Utilization Ø        Revenue targets and cost limitations are manageable Ø        Operating activities are efficient and wealth-maximizing Ø        Tax and pension payments will be on-time Ø        Capital spending can be minimized without altering returns by favoring more important operational needs Ø        Short-term liabilities and other payments are paid when due without hurting credit rating due to questions on solvency Seeking Consultancy Services Ø        Divisions/ subsidiaries can maximize their revenue potential and minimize their operating costs   Dissolution of Ineffective Partnerships Ø        Maximize investing potentials both direct and portfolio investments Ø        Improving the rationale behind selling stocks Ø        Share repurchases can be conducted with rigid planning     Future Expectations: From Bad to Good and Good to Better             Apply decentralized treasury function.  When each department/ division budget is centralized, the financing and investing strategies will be consistent to the overall strategy of the firm ( 1999).  This will also result to larger volumes of cash that might reduce bank charges and interest rates.  As the firm has higher interest expense that interest income for the last three years amounting at 0 million to 0 million, the economies of scale of a centralized treasury might alleviate some of the negative financial accounts of the firm due to this cost saving strategy.  However, cost leadership strategy cannot maximize the revenue potential of a firm and its growth ( 2003).  Decentralized treasury function allows the company to be flexible and more responsive to its global operations, reduce bureaucracy hence obtain efficiency and performance evaluation of local managers ( 1999).  More importantly, these characteristics will sustain the differentiation strategy of the firm which intends to maximize its revenue and growth potential.               In considering strategic and tactical outcomes, decentralized treasury will make different country subsidiaries independent to its headquarters.  This may have implications on its own pricing strategy which involve economic factors in their specific location.  In a similar case, centralized advertising budget (in which Pepsi is known to highlight celebrity figures) may not be effective in other cultures due to local taboos.  The scandals of Madonna and Michael Jackson that received demerit and criticism from the Catholic Church also suggested that global promotions in general and use of known celebrities in particular would not always stimulate demand rather result to unintended de-marketing.  The substantial budget provided to these celebrities that might as well distributed across different geographical subsidiaries to maximize their use.               Lastly, the performance of different country subsidiaries will be evaluated more objectively while the performance appraisal of the headquarters will be more enforceable.  Unlike centralized treasury which is volatile to pass-over accountability, decentralized structure gives subsidiaries their freedom to choose their goals, create and implement their own strategies to achieve them and use the budget the headquarters approved.  The electric motors and computer support systems manufacturer Emerson had succeeded in using the same application to its global units that impacted its 30-year continuous growth in profit and stock value ( 1998).  The budgeting model of Emerson allows its business managers to plan, execute and deliver their goals using their own creativity with minimal headquarter intervention unless a major concern.  When applied to the firm, managers will see their budgets and budget utilization as the reflection of their reputation as well as the reputation of their subsidiaries.               Use performance-based budgeting.  This is the component required for a decentralized treasury to function effectively.  When the organization is decentralized, competition can exist among divisions and subsidiaries to maximize their budget request and ceiling at the beginning of the next operations.  When this happens, it is probable that motivation can vanish when one division feels that their performance is trailing far behind of its peer division.  However, when performance evaluation and budget provision is based on the mission of a specific division and their pre-determined results, competitive and de-motivation tendencies can be prevented.  Performance-based budgeting requires a division/ subsidiary to cost each of their activity/ project and determine the intended results after implementation ( 2001).  When this is accomplished, decentralized structure within the global firm can be easily deployed since each division has a goal in mind with less regard to peer competition.    Conclusion             Pepsi’s current financial situation is observed to have specific loopholes and sub-optimal performance particularly in financial accounts such as cost of sales, portfolio investments, debts and PepsiCo International.  However, with the introduction of budget control techniques, the firm has able to cut down on costs, establish weal-maximizing investments, avoid excessive debts due to efficiency, and improve division/ subsidiary output.  In this view, it can be said that Pepsi is one organization who benefit so much from budget control.  Further, this implies the vitality of financial approach to a global firm profitability and long-term growth.  As illustrated, if the firm continued its Sichuan (China) venture, it will loose tract on subsidiary performance that connotes financial inaccuracy.  As numbers do not lie because they have their exact values, decisions that can be derived from such condition are tantamount to integrate inaccuracies to the whole organizational units.  Lastly, it is also suggestive that decentralized treasury coupled with performance based budgeting can enhance the viability of budget control to be able for Pepsi to compete in a duopoly global cola market.                  Bibliography   Credit:ivythesis.typepad.com

ASSIGNMENT ON IMPROVING DEPARTMENTAL FINANCIAL MANAGEMENT

Introduction This paper highlights a global firm, Pepsi, not to discuss how it outperformed Coca Cola in a recent Forbes pre...

Measuring Single-Asset Risk

Measuring Single-Asset Risk             Standard deviation is a statistical measure of dispersion around an expected value ( 1999).  With this, risks can be derived from standard deviation and returns to expected value.  It is unlikely that an investor would place his money to single-asset, as such cannot be hedged by diversification, except on specific contracts.  In HKSE, 1-month HIBOR future (2005) is an example of single-asset usually obtained by a buyer who wants to transfer the risk from interest rate fluctuations.  He probably has huge debt from local banks and his interest payments depend largely on interest rates of such banks in which are continuously changing.                To measure the risk position of the buyer, it is necessary to determine individual returns which depends to interest rate-sensitive indicators, say, Hong Kong’s levels of FDI and the probability of their occurrence.  Let us assumed that the buyer after thorough research has classified high, medium and low FDI levels with probabilities of occurrence of 25%, 50% and 25% respectively and probable returns at 15%, 12% and 8% respectively.  After calculating the expected value of a return, risk measurement can be conducted by deriving it from standard deviation (see computation 1).               The computation shows that the expected value of the buyer’s return is 11.75% and his risk is 2.49%.  Statistically, using the normal probability distribution (see figure 1), it can said that there is 68% chance that the actual return will lie within ±1σ of 11.75% (the mean) and 95% chance within ±2σ of 11.75%.  However, determining the risk of the venture has yet to be completely derived.  The normal distribution merely mimic the rule of return-risk trade-offs.  In ±1σ scenario, there is smaller dispersion (risk) coupled with smaller upper limit of 14.24% but minimal lower limit of 9.26%.  In contrast, the ±2σ scenario shows that there is higher dispersion (risk) coupled with larger upper limit of 16.73% but too low lower limit of 6.77%.  Question of investment alternatives become useful to this finding to obtain comparative statistics.  At this moment, the investor can simply assess his attitude to risk with reference to vital factors, say, his liquidity.        Measuring Portfolio Risk             Extending the analysis of the cautionary finding in the preceding example, we can derive the risk position of the buyer with more accuracy when we will also compute for another type of asset alternative (say, the 3-month HIBOR futures).  Assuming that the buyer opted to have follow-up research for this and come-up with information in Table 1, which for the purpose of comparison, situated beside the 1-month HIBOR futures.  It can be observed that 3-month HIBOR future (HKSE website 2005) is more sensitive since it can be classified narrowly to very high FDI, high FDI, moderately high FDI, and so on.  This, possibly, is caused by higher risk (and return) attached with longer exposure to market and economy fluctuations.               In computing for the expected value and standard deviation of the 3-month HIBOR (see computation 2), it is still contestable what is the optimal investment destination.  This can be answered by coefficient of variation (see computation 3).  Thus, the 3-month HIBOR future is computed not only the less risky investment option but more profitable than the 1-month HIRBOR computed earlier.  Someone would ask, where did the expected value of return will come from noting that the purpose of such purchase is for the buyer to offset substantial fluctuations of banks’ interests rates where he has outstanding loans and interest payments?  This can be resolved for the fact that those HIBORs are also tradable where a large amount in a transaction would not only shield the buyer from interest rate shocks but also derive profits (losses) from them.                 Four Ways of Common Stock Valuation Zero and Constant Dividend Growth             Expectations on future dividend payments primarily characterize the value of ordinary (common) shares.  This is an assumption that the firm will not be sold or take-over to/by another firm (p. 260).  Figure 2 shows the basic formula to determine common stock value.  However, since firm performance and consequently its dividend payments can only be estimated, placing a numerical value in the formula may lead shareholders to exaggeration or even underestimation.  Due to this, there are two specific assumptions for guidance; namely, zero dividend growth and constant dividend growth (p. 261).                For example, assuming that an HKSE listed firm Esprit is expected to pay a dividend of HK.50 indefinitely and the required rate of return is 12%.  As observed, the expected dividend is termed as ‘indefinitely’ to acknowledge that no growth will ensue in the meantime probably such is applicable to some countries in the European market of Esprit due to stiff competition (Esprit website 2006).  By canceling the period of varying dividend growth, the figure 2 formula would simply derive the answer from the quotient of expected dividend per share and required rate of return equivalent to HK.17.  On the other hand, assuming that the new woman’s apparel of the firm has enticed the North American market that resulted to expected constant dividend growth of 5% per year.  Using figure 2, the answer is HK$ 7.50.    As observed, the positive reaction of North American market indirectly increased the stock value primarily due to higher expected future cash flows.  However, such assumptions should not be easily taken by shareholders since the crucial part of the computation lies in accurate finding of the required rate of return and dividend growth.  The former will be tackled in the later discussion about cost of capital while the latter can be derived using the next discussion about growth dividend estimation.    Estimating the Growth Rate of Dividend             For example, an investor is confronted with Esprit financial information as follows:                                             Appendices     Computation 1                             E(r)=r1 P(r1 )+r2 P(r2 )+…+rn P(rn ) where, ri = rate of return for the identified ith outcome P(ri) = probability of earning return i for the identified outcome n = number of possible outcomes   So,     E(r) = 0.25(15%)+0.50(12%)+0.25(8%) = 11.75%       where Var(r ) = the variance of returns σr = the standard deviation of returns r̄ = the expected or mean value of a return ri = return for the ith outcome P(ri ) = probability of occurrence of the ith outcome n = number of outcomes considered       (2)−(3) (4)×(4)   (5)×(6) (1) (2) (3) (4) (5) (6) (7) I ri r̄ ri−r̄ (ri−r̄)2 P(ri) (ri−r̄)2×P(ri) 1 15% 11.75% 3.25% 10.56% 0.25 2.64% 2 12 11.75 0.25 0.06 0.50 0.03 3 8 11.75 −3.75 14.06 0.25 3.52     Finally, our standard deviation is 2.49%.          Computation 2     Rate of Return Probability of Occurrence Expected Value           6 0.05 12 -6 36 1.8     8 0.1 -4 16 1.6     10 0.2 -2 4 0.8     12 0.3 0 0 0     14 0.2 2 4 0.8     16 0.1 4 16 1.6     18 0.05 6 36 1.8               8.4 2.89%                                                                                       1-month 3-month Expected value 11.75% 12 Std deviation 2.49% 2.89%                 Computation 3       1-month 3-month Expected value 11.75% 12 Std deviation 2.49% 2.89% Coefficient of Variation 0.211915   0.002408                                 Computation 4   Computation High-Decline-Stable   Next, we value the stable growth period: DPS = .00 (1.06) = .12 Ks = 12.8% g = 6% .12 / (.128-0.06) = .18 Next, we must calculate the present value of the dividends. .18 / (1.1239)5 = .39 When calculating the present value of the dividends of the stable growth period, we use the same required rate of return as the high-growth phase and raise it to the fifth power for a five-year example like the one above. Adding the two values, we get: .39 + .94 = .33                     Figure 1                     Figure 2   Formula of basic equity valuation model   The basic equity share valuation model is given by: 4 where, SV0 = value (price) of the share at time zero Dt = expected dividend per share (DPS) at end of year t (t=1, 2, …, n, …, ∞) r = required annual rate of return on the share/discount rate ∞ = symbol denoting infinity     Zero Growth       Constant Growth   Figure 3 E(ri )=Rf +βi (ERm −Rf ) where, E(ri ) = required return on asset/share i Rf = risk-free rate of return βi = beta coefficient for asset/share i ERm = expected market return, that is the return expected on the market portfolio of shares       Table 1   Asset A Asset B Rate of return (%) Probability of occurrence, P(ri) Rate of return (%) Probability of occurrence, P(ri) 6 0.05 8 0.25 8 0.10 10 0.50 10 0.20 12 0.25 12 0.30     14 0.20     16 0.10     18 0.05             Table 2: Future value interest factor (FVIF) for £1 compounded at r per cent for n periods (p. 695)     n 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 1.110 1.120 1.130 1.140 1.150 1.160 1.170 1.180 1.190 1.200 2 1.232 1.254 1.277 1.300 1.322 1.346 1.369 1.392 1.416 1.440 3 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 1.728 4 1.518 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005 2.074 5 1.685 1.762 1.842 1.925 2.011 2.100 2.192 2.288 2.386 2.488 6 1.870 1.974 2.082 2.195 2.313 2.436 2.565 2.700 2.840 2.986 7 2.076 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379 3.583 8 2.305 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021 4.300 9 2.558 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785 5.160 10 2.839 3.106 3.395 3.707 4.046 4.411 4.807 5.234 5.695 6.192 11 3.152 3.479 3.836 4.226 4.652 5.117 5.624 6.176 6.777 7.430 12 3.498 3.896 4.334 4.818 5.350 5.936 6.580 7.288 8.064 8.916 13 3.883 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596 10.699 14 4.310 4.887 5.535 6.261 7.076 7.987 9.007 10.147 11.420 12.839 15 4.785 5.474 6.254 7.138 8.137 9.265 10.539 11.974 13.589 15.407 16 5.311 6.130 7.067 8.137 9.358 10.748 12.330 14.129 16.171 18.488 17 5.895 6.866 7.986 9.276 10.761 12.468 14.426 16.672 19.244 22.186 18 6.543 7.690 9.024 10.575 12.375 14.462 16.879 19.673 22.900 26.623 19 7.263 8.613 10.197 12.055 14.232 16.776 19.748 23.214 27.251 31.948 20 8.062 9.646 11.523 13.743 16.366 19.461 23.105 27.393 32.429 38.337 21 8.949 10.804 13.021 15.667 18.821 22.574 27.033 32.323 38.591 46.005 22 9.933 12.100 14.713 17.861 21.644 26.186 31.629 38.141 45.923 55.205 23 11.026 13.552 16.626 20.361 24.891 30.376 37.005 45.007 54.648 66.247 24 12.239 15.178 18.788 23.212 28.625 35.236 43.296 53.108 65.031 79.496 25 13.585 17.000 21.230 26.461 32.918 40.874 50.656 62.667 77.387 95.395 30 22.892 29.960 39.115 50.949 66.210 85.849 111.061 143.367 184.672 237.373 40 64.999 93.049 132.776 188.876 267.856 378.715 533.846 750.353 1051.642 1469.740 50 184.559 288.996 450.711 700.197 1083.619 1670.669 2566.080 3927.189 5988.730 9100.191     </div> Credit:ivythesis.typepad.com

Measuring Single-Asset Risk

Measuring Single-Asset Risk Standard deviation is a statistical measure of dispersion around an expected value ( 1999). With...