A snakes and ladders representation of stock prices and returns

Snakes and ladders is an ancient Indian game of chance that offers amusement as well as a metaphor for life’s many ups and downs. Games offer useful and fun ways of conveying ideas as well as solution techniques and this game has considerable mathematical tractability. This note shows how snakes and ladders can be used to represent the ups and downs of share ownership and solve for fair values of a multistage project that pays fixed dividends at uncertain completion times and has random returns

Chronology for climate change: Developing age models for the biogeochemical ocean flux study cores

We construct age models for a suite of cores from the northeast Atlantic Ocean by means of accelerator mass spectrometer dating of a key core, BOFS 5K, and correlation with the rest of the suite. The effects of bioturbation and foraminiferal species abundance gradients upon the age record are modeled using a simple equation. The degree of bioturbation is estimated by comparing modeled profiles with dispersal of the Vedde Ash layer in core 5K, and we find a mixing depth of roughly 8 cm for sand-sized material. Using this value, we estimate that age offsets between unbioturbated sediment and some foraminifera species after mixing may be up to 2500 years, with lesser effect on fine carbonate (<10 mu m) ages. The bioturbation model illustrates problems associated with the dating of ''instantaneous'' events such as ash layers and the ''Heinrich'' peaks of ice-rafted detritus. Correlations between core 5K and the other cores from the BOFS suite are made on the basis of similarities in the downcore profiles of oxygen and carbon isotopes, magnetic susceptibility, water and carbonate content, and via marker horizons in X radiographs and ash beds

Northeastern Atlantic benthic foraminifera during the last 45,000 years: Changes in productivity seen from the bottom up

We studied benthic foraminifera from the last 45 kyr in the >63 mu m size fraction in Biogeochemical Ocean Flux Studies (BOFS) cores 5K (50 degrees 41.3'N, 21 degrees 51.9'W, depth 3547 m) and 14K (58 degrees 37.2'N, 19 degrees 26.2'W, depth 1756 m), at a time resolution of several hundreds to a thousand years. The deepest site showed the largest fluctuations in faunal composition, species richness, and benthic foraminiferal accumulation rates; the fluctuations resulted from changes in abundance of Epistominella exigua and Alabaminella weddellensis. In the present oceans, these species bloom opportunistically when a spring plankton bloom results in seasonal deposition of phytodetritus on the seafloor. The ''phytodetritus species'' had very low relative abundances and accumulation rates during the last glacial maximum. A strong increase in absolute and relative abundance of E. exigua and A weddellensis during deglaciation paralleled the decrease in abundance of the polar planktonic foraminifer Neogloboquadrina pachyderma (s), and the increase in abundance of warmer water planktonic species such as Globigerina bulloides. This strong increase in relative abundance of the ''phytodetritus species'' and the coeval increase in benthic foraminiferal accumulation rate were thus probably caused by an increase in the deposition of phytodetritus to the seafloor (and thus probably of surface productivity) when the polar front retreated to higher latitudes. The abundance of ''phytodetritus species'' decreased during the Younger Dryas, but not to the low levels of fully glacial conditions. During Heinrich events (periods of excessive melt-water formation and ice rafting) benthic accumulation rates were very low, as were the absolute and relative abundances of the ''phytodetritus species'', supporting suggestions that surface productivity was very low during these events. In both cores Pullenia and Cassidulina species were common during isotope stages 2, 3 and 4, as were bolivinid, buliminid and uvigerinid species. High relative abundances of these species have been interpreted as indicative either of sluggish deep water circulation or of high organic carbon fluxes to the seafloor. In our cores, relative abundances of these species are negatively correlated with benthic foraminiferal accumulation rates, and we can thus not interpret them as indicative of increased productivity during glacials. The percentage of these ''low oxygen'' species calculated on a ''phytodetritus species'' - free basis decreased slightly at deglaciation at 5K, but not at 14K. This suggests that decreased production of North Atlantic Deep Water during the last glacial might have slightly affected benthic foraminiferal faunas in the eastern North Atlantic at 3547 m depth, but not at 1756 m. In conclusion, major changes in deep-sea benthic foraminiferal faunas over the last 45,000 years in our cores from the northeastern Atlantic were the result of changes in surface water productivity, not of changes in deep water circulation; productivity was lower during the glacial, probably because of extensive ice cover

Empirical pricing kernels obtained from the UK index options market

Empirical pricing kernels for the UK equity market are derived as the ratio between risk-neutral densities, inferred from FTSE 100 index options, and historical real-world densities, estimated from time series of the index. The kernels thus obtained are almost compatible with a risk averse representative agent, unlike similar estimates for the US market

Early Neoproterozoic limestones from the Gwna Group, Anglesey

Limestone megaclasts up to hundreds of metres in size are present within the Gwna Group mélange, North Wales, UK. The mélange has been interpreted as part of a Peri-Gondwanan fore-arc accretionary complex although the age of deposition remains contentious, proposals ranging from Neoproterozoic to Early Ordovician. This paper uses strontium isotope chemostratigraphy to establish the age of the limestone blocks and thus provide a maximum age constraint on mélange formation. Results show that, although the carbonates are locally dolomitized, primary 87Sr/86Sr ratios can be identified and indicate deposition sometime between the late Tonian and earliest Cryogenian. This age is older than that suggested by stromatolites within the limestone and indicates that the limestone did not form as cap carbonate deposits

Buyback Behaviour and the Anti-Dilution of Dilutive Stock Options

Paper presented at 2016 FMA Annual Meeting, October 19-22, 2016, Las Vegas, NevadaWe study how dilutive board-level stock options impact anti-dilutive daily buybacks in the UK. We show that buyback behaviour and stock option holdings positively influence cumulative post-buyback returns. Buybacks, however, have anti-dilutive implications and are thus linked to the level and nature of dilutive stock options outstanding. We find increases in aggregate stock options to escalate buyback implementation. This is driven largely by unvested stock options that significantly enhance anti-dilutive benefits. Robustness tests using “overconfident” board classification and treasury share regulation confirm the anti-dilutive motive behind buybacks when stock options are unvested

Risk-based school inspections: impact of targeted inspection approaches on Dutch secondary schools

In most countries, publicly funded schools are held accountable to one inspectorate and are judged against agreed national standards. Many inspectorates of education have recently moved towards more proportional risk-based inspection models, targeting high-risk schools for visits, while schools with satisfactory student attainment levels are excluded from inspections. This paper looks into these newer inspection models and aims to enhance our understanding of the potential effectiveness of such targeted models on student attainment and other performance indicators. Random effects models, analyzing changes in schools over time, indicate that targeted inspections particularly have an effect on student attainment in literacy in weak schools, while also impacting on student satisfaction, student numbers and student-staff ratios

Continuous Workout Mortgages

This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable "workout proportion" and adjustable "workout threshold." These results are of importance as they not only help understanding the mechanics of CWMs and estimating key contract parameters. These results are of importance as they not only help in the understanding of the mechanics of CWMs and estimating key contract parameters, but they also provide guidance on how to enhance the resilience of the financial architecture and mitigate systemic risk.Continuous Workout Mortgage (CWM), Repayment, Interest-only, House price index, Prepayment intensity, Cap and floor on continuous flow

The prevalence of use and value of wild edible herbs in South Africa

The prevalence of use and commercial value of wild edible herbs in South Africa is examined from four recent quantitative studies at eight different sites. The use of wild edible herbs was widespread in rural communities, with over 90% of households using them in all but one sample site. Mean frequency of use in season was generally between two and five times per week, with a mean of four times across all sites. But many households consume them daily. Use in winter was less than in summer. The mass of wild edible herbs consumed ranged from 12 kg to over 130 kg per household per year. Local (farm-gate) prices ranged from R2.65 to R72 per kilogram, but were generally between R30 and R40 per kg. Direct-use value to consuming households ranged from R85 to almost R5000 across the eight sites, with a mean of R1020 per user household per year. Although harvesting of wild herbs takes time, the high gross direct-use value represents a considerable saving on having to purchase commercial alternatives. Key species differ from place to place both in availability and use, and include both indigenous and exotic species. Commonly used genera include Amaranthus, Bidens, Chenopodium, Cleome, Corchorus, and Momordica. The use, value and trade in wild edible herbs currently receives no recognition in land and agrarian reform policies. It is imperative that this be addressed, and the relationships between rural livelihoods, use of wild edible herbs, food security, and land and resource tenure be clarified, and debated within the policy forums around different models for, and delivery of, agrarian reform and rural development

Will the real custodian of natural resource management please stand up

South Africa is the custodian of an immense wealth of biodiversity resources, and is estimated to be the third most biodiverse country in the world. At the ecosystem level this biodiversity supports the production of goods and services used by us all; water, air, soil fertility, wood, food, etc. At a more local level the harvesting of numerous natural resources provides consumptive products for millions of poor South Africans, as well as income for equally significant numbers.Consumption of and trade in these resources is the very mainstay of their well-being, and crucial in preventing deeper poverty levels. For example, despite massive improvements in the provision of electricity, most rural and a significant proportion of urban South Africans continue to use fuelwood as a key energy source for cooking (e.g. 65% of electrified households in the urban areas of Makana municipality, and 92% of households in the rural areas of Bushbuckridge); approximately 75% of the population use medicinal plants for medicinal or cultural reasons; and millions of urban and rural households make use of wild edible herbs. With such high demand for these resources, it is not unsurprising that there are large and established trade networks spanning local, regional, national and, for some resources (e.g. specific medicinal plants, mopane worms), international boundaries. The total value of this trade is unknown, and unrecorded in local or national economic or GDP statistics. It certainly equates to billions of rands per year. The direct-use and trade values are substantial and provide a cost saving to the State. Where biodiversity resources are overused or exhausted, people have to purchase alternatives, which reduces their scarce cash resources, thereby increasing their likely dependency on State welfare grants