# Fish farming

When we in 2002 were asked to look into the risk of Cod fish farming, we had to start with the basics; how do cod feed and grow at different locations and what is the mortality at the same locations.

The first building block was Björn Björnsson’s paper; Björnsson, B., Steinarsson, A., Oddgeirsson, M. (2001). Optimal temperature for growth and feed conversion of immature cod. ICES Journal of Marine Science, 58: 29-38.

Together with: Björn Björnsson, Marine Research Institute, Iceland and Nils Henrik Risebro, University of Oslo, Norway we did the study presented in the attached paper – Growth, mortality, feed conversion and optimal temperature for maximum rate of increase in biomass and earnings in cod fish farming. (Growth, mortality, feed conversion and optimal temperature for maximum …..)

This formed the basis for a stochastic simulation model used to calculate the risk in investing in cod fish farming at different locations in Norway.

The stochastic part was taken from the “estimation errors” for the relations between growth, feed conversion, mortality etc. as function of deviation from optimal temperature.

As optimal temperature varies with cod size, temperature at a fixed location will during the year and over the production cycle deviate from optimal temperature. Locations with temperature profiles close to optimal temperature profile for growth in biomass will, other parameters held constant, are more favorable.

The results that came out favorably for certain locations were subsequently used as basis for an IPO to finance the investment.

The use of the model was presented as an article in Norsk Fiskeoppdrett 2002, #4 and 5. It can be downloaded here **(See: Cod fish farming)**, even if it is in Norwegian some of the graphs might be of interest.

The following graph sums up the project. It is based on local yield in biomass relative to yield at optimal temperature profile for growth in biomass. Farming operation is simulated on different locations along the coast of Norway and local yield and its coefficient of variation (standard deviation divided by mean) is in the graph plotted against the locations position north. As we can see is not only the yield increasing as the location moves north, but also the coefficient of variation, indicating less risk in an investment.

The temperature profile for the locations was taken from the Institute of Marine Research publication: Hydrographic normals and long – term variations at fixed surface layer stations along the Norwegian coast from 1936 to 2000, Jan Aure and Øyvin Strand, Fisken og Havet, #13, 2001.

Locations of fixed termografic stations along the coast of Norway.

The study gives the monthly mean and standard deviation of temperature (and salinity) in the surface layer at the coastal stations between Sognesjøen and Vardø, for the period 1936 – 1989.

Monthly mean of temperature in the surface layer at all stations

By employing a specific temperature profile in the simulation model we were able to estimate the probability distribution for one cycle biomass at that location as given in the figure below.

Having the probability distribution for production we added forecasts for cost and prices as well as for their variance. The probability distributions for production also give the probability distribution for the necessary investment, so that we in the end were able to calculate the probability distribution for value of the entity (equity).