Non-linear dynamics of double-cavity optical bistability of three-level ladder system

We present non-linear dynamical features of two-photon double-cavity optical bistability exhibited by a three level ladder system in the mean field limit. The system exhibits a hump like feature in the lower branch of the bistable response, wherein a new region of instability develops. The system displays a range of dynamical features varying from normal stable switching, periodic self-pulsing to a period-doubling route to chaos. The inclusion of two competing cooperative atom-field couplings leads to such rich nonlinear dynamical behavior. We provide a domain map that clearly delineates the various regions of stability that will aid the realization of any desired dynamics. We also present bifurcation diagram and the associated supporting evidence that clearly identifies the period-doubling route to chaos, which occurs at low input light levels.Comment: 7 Pages, 9 figures. Feedback is welcom

Estimating Risk Parameters

Over the last three decades, the capital asset pricing model has occupied a central and often controversial place in most corporate finance analysts’ tool chests. The model requires three inputs to compute expected returns – a riskfree rate, a beta for an asset and an expected risk premium for the market portfolio (over and above the riskfree rate). Betas are estimated, by most practitioners, by regressing returns on an asset against a stock index, with the slope of the regression being the beta of the asset. In this paper, we attempt to show the flaws in regression betas, especially for companies in emerging markets. We argue for an alternate approach that allows us to estimate a beta that reflect the current business mix and financial leverage of a firm

Optical instabilities in three-level lambda and V system inside double-cavity

We obtain optical instabilities in all-optical bistable systems arising from competing cooperative pathways at low input light levels. In particular for three-level atomic systems in the lambda and V configuration interacting with two independent cavity modes, we identify the necessary conditions related to the incoherent pathways required to obtain instabilities. The instabilities arise when atomic states involved in the bistable transition are leaky and have substantial population, where the incoherent processes adversely affect the cooperative behavior of the atomic ensemble.Comment: Comments can be sent to [email protected]

Negative and positive hysteresis in double-cavity optical bistability in three-level atom

We present novel hysteretic behaviour of a three-level ladder atomic system exhibiting double-cavity optical bistability in the mean-field limit. The two fields coupling the atomic system experience feedback via two independent, unidirectional, single mode ring cavities and exhibit cooperative phenomena, simultaneously. The system displays a range of rich dynamical features varying from normal switching to self pulsing and a period-doubling route to chaos for both the fields. We focus our attention to a new hump like feature in the bistable curve arising purely due to cavity induced inversion, which eventually leads to negative hysteresis in the bistable response. This is probably the only all-optical bistable system that exhibits positive as well as negative bistable hysteresis in different input field intensity regimes. For both the fields, the switching times, the associated critical slowing down, the self-pulsing characteristics, and the chaotic behaviour can be controlled to a fair degree, moreover, all these effects occur at low input light levels.Comment: 5 Pages, 3 figures. Feedback is welcom

Estimating Equity Risk Premiums

Equity risk premiums are a central component of every risk and return model in finance. Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. The standard approach to estimating equity risk premiums remains the use of historical returns, with the difference in annual returns on stocks and bonds over a long time period comprising the expected risk premium, looking forward. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to limited and noisy. We suggest ways in which equity risk premiums can be estimated for these markets, using a base equity premium and a country risk premium. Finally, we suggest an alternative approach to estimating equity risk premiums that requires no historical data and provides updated estimates for most markets

Dealing with Operating Leases in Valuation

Most firm valuation models start with the after-tax operating income as a measure of the operating income on a firm and reduce it by the reinvestment rate to arrive at the free cash flow to the firm. Implicitly, we assume that the operating expenses do not include any financing expenses (such as interest expense on debt). While this assumption, for the most part, is true, there is a significant exception. When a firm leases an asset, the accounting treatment of the expense depends upon whether it is categorized as an operating or a capital lease. Operating lease expenses are treated as part of the operating expenses, but we will argue that they really represent financing expenses. Consequently, the operating income, capital, profitability and cash flow measures for firms with operating leases have to be adjusted when operating lease expenses get categorized as financing expenses. This can have significant effects not just on valuation model inputs, but also on some multiples such as Value/EBITDA ratios that are widely used in valuation

Financing Innovations and Capital Structure Choices

The last two decades have seen a stream of innovation in financial markets, especially in the corporate bond arena. Some of these innovations were designed to give firms more flexibility in designing cash flows on borrowings, allowing them to match up cash flows on financing more closely to cash flows on assets, thus increasing their debt capacity. These changes have been for the most part good news for corporate treasurers, but the relentless torrent of innovation has also resulted in some firms issuing these new and more complex securities for the wrong reasons. Some have done so to keep up with other firms in their peer group, and other to take advantage of loopholes in the way ratings agencies and regulatory agencies define debt and equity. In this context, it is worth noting that as corporate bonds have become more complex, investment bankers once more become indispensable to the process, proving both pricing and selling support. It is important that firms recognize when complexity serves their interests, and when it can end up hurting them

Research and Development Expenses: Implications for Profitability Measurement and Valuation

Most valuation models begin with a measure of accounting earnings to arrive at cash flow estimates. When using accounting earnings, we implicitly assume that the income is obtained by netting out only those expenses that are operating expenses, i.e., expenses designed to generate revenues in the current period. Expenses that are intended to provide benefits over multiple periods are assumed to be considered as capital expenditures, and these expenses are depreciated or amortized over multiple periods. In addition, when computing profitability measures such as return on equity and capital, we stick with this assumption that operating income measures income generated by assets in place. In this paper, we examine the accounting treatment of research and development expenses, and the effects of the treatment on operating income, capital and profitability. We argue that research and development expenses should be treated as tax-deductible capital expenditures, for purposes of valuation, and this can have significant effects on operating income, capital and expected growth measures for firms with substantial research expenses

Estimating Risk Parameters

Over the last three decades, the capital asset pricing model has occupied a central and often controversial place in most corporate finance analysts’ tool chests. The model requires three inputs to compute expected returns – a riskfree rate, a beta for an asset and an expected risk premium for the market portfolio (over and above the riskfree rate). Betas are estimated, by most practitioners, by regressing returns on an asset against a stock index, with the slope of the regression being the beta of the asset. In this paper, we attempt to show the flaws in regression betas, especially for companies in emerging markets. We argue for an alternate approach that allows us to estimate a beta that reflect the current business mix and financial leverage of a firm