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# 金融代写|投资组合代写Investment Portfolio代考|Allocating Wealth Across Goals and Across Investments

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## 金融代写|投资组合代写Portfolio Theory代考|Allocating Wealth Across Goals and Across Investments

Granularity is an obvious question at this stage-more granularity is better, but we can quickly run into unreasonable computation times and memory needs. If $\varrho$ is our level of resolution $(\varrho=100$ for $1 \%$ intervals, $\varrho=20$ for $5 \%$ intervals, $\varrho=10$ for $10 \%$ intervals, etc.) and $N$ is the number of goals, then we must calculate and hold in memory $\varrho \times N$ portfolios. Five goals run with a resolution of 100 yields $5 \times 100=500$ portfolio calculations that must be made and held in memory. In the end, the practitioner has to make this decision based on the application at hand and the computational resources available. It may well be that a resolution of 20 or 10 is sufficient for a particular application. I do not believe there is one right answer here.

Once we have generated optimal portfolios for each goal given each potential level of wealth, we use the results of these optimal investment allocations to inform the optimal across-goal allocation. Because of the discrete nature of our portfolio allocation results, I recommend using a Monte Carlo engine to simulate various across-goal allocations and their effects on total utility. Obviously, we are trying to find the across-goal allocation that yields the highest utility. For each simulation of across-goal allocation, we match the optimal portfolio for that level of across-goal allocation and return a probability of achievement. That probability is the input used in the utility function.

Finally, we match the optimal across-goal allocation with the optimal within-goal portfolio weights and return the optimal aggregate portfolio (or keep them separate, whichever the implementation strategy demands).

That is the procedure summary. Now, let’s tackle the first-stage optimization algorithm.
Define:
investment universe of $k$-number of potential investments.
necessary level of resolution, $\log$ this as $\varrho .^2$
$\pi(\omega)$ returns the parameters of our chosen cdf, given portfolio weights, $\omega .{ }^4$ parameters

## 金融代写|投资组合代写Portfolio Theory代考|CASE STUDY

Let’s consider a case study together to help illustrate the procedure. For interested readers, I have included the relevant $\mathrm{R}$ code script as part of the book supplement. Again, I want to stress that the actual procedure may not be optimal from a computational perspective-I would encourage other practitioners and researchers to develop their own approach-but it suffices for my purposes.

A client joins our firm. Our first step as advisors is to spend ample time in conversation. We need to fully understand her goals, her tax situation, her ethical constraints (more on that later), and so on. We must also ensure that she has reasonable expectations, both of herself and us. We should never take on a client with unreasonable expectations or a client mandate that is not within our ability. This conversation is, then, a two-way street, determining whether this client will fit within our process as well as for the client to get a handle on her financial goals and financial picture.

Another objective at this stage is to help the client dream a little. I have found that, very often, clients do not have a clear picture of their goals. One of an advisor’s jobs is to help the client crystalize her objectives. They are changeable, of course, and communicating that point is important, as well; clients will have a harder time committing to 30 -year objectives that they feel can never be updated. This involves plenty of listening as clients talk themselves through their needs, wants, wishes, and dreams. We need to spend time forecasting our client’s psychological state (“how would you feel if. ..”), as well as forecasting their financial state (“what is your pattern of raises…”). Client homework is not uncommon after the first meeting or two.

After ample conversation, we determine that our new client has the following goals in her goals-space:

• She wants to leave an estate to her children of $\$ 5,000,000$, planned in 30 years from now. • She needs to maintain her lifestyle expenses starting in 10 years, and we estimate that she will need$\$5,157,000$ to do that.
• Our client would like to purchase a vacation home in 4 years, and her estimated price is $\$ 713,500$. • If possible, our client would like to donate$\$8,812,000$ to her alma mater sometime around 18 years from now. This donation carries naming rights to a building on campus.

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